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How Large is the Wealth Effect for South Africa?

An empirical investigation into the relationship between consumption, wealth, and income in the South African economy, and the implications of this relationship on monetary policy.

A Research Report Presented to The University of Cape Town 10 December 2010

Masters in Business Administration (Full-Time)

Rihaan Samuel (FT465) Student Number: smlrih001

Supervisor: Mr. S.J. Gossel

Co-supervisor: Dr. Mills Soko

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TABLE OF CONTENTS

I. LIST OF FIGURES ..................................................................................... 4

II. LIST OF TABLES ....................................................................................... 5

III. LIST OF ABBREVIATIONS ...................................................................... 6

IV. ABSTRACT ................................................................................................ 7

V. ACKNOWLEDGEMENTS ......................................................................... 8

VI. PLAGIARISM DECLARATION ................................................................ 9

1. INTRODUCTION ..................................................................................... 11

Government and Private Saving in South Africa .............................................................................. 12

Monetary Policy in South Africa ...................................................................................................... 13

Household Wealth, Income and Consumption in South Africa ........................................................ 15

2. RESEARCH QUESTIONS AND SCOPE ................................................. 26

Research Question and Sub-Questions: ............................................................................................ 26

Research Assumptions ...................................................................................................................... 27

3. LITERATURE REVIEW .......................................................................... 28

Discussion ......................................................................................................................................... 28

Modelling Consumption – The Underlying Theory ......................................................................... 29

The Optimal Consumption Path and the Life-Cycle Model ......................................................... 30

Optimal Consumption Path ....................................................................................................... 30

Life-cycle Model ....................................................................................................................... 31

Effects of Stock Market Wealth on Consumption ........................................................................ 32

Effects of Housing Wealth on Consumption ................................................................................ 33

Review of the Empirical Literature ................................................................................................... 34

Ludvigson and Steindel (1999) ..................................................................................................... 34

Lettau and Ludvigson (2001) ........................................................................................................ 37

Lettau and Ludvigson (2004) ........................................................................................................ 38

Literature Based on Lettau and Ludvigson (2004) ...................................................................... 39

Existing Empirical Studies for South Africa ................................................................................. 39

Conclusion ........................................................................................................................................ 40

Selected approach ......................................................................................................................... 41

Research Hypotheses .................................................................................................................... 41

4. RESEARCH METHODOLOGY ............................................................... 44

Research Approach and Strategy ...................................................................................................... 44

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Review of Methodologies in the Empirical Literature ...................................................................... 45

Research Design................................................................................................................................ 48

Variable Measure Selection and Data Collection: ........................................................................ 48

Consumption ............................................................................................................................. 48

Wealth ....................................................................................................................................... 51

Income....................................................................................................................................... 52

System Selection ....................................................................................................................... 53

Criticism of System 2 ................................................................................................................ 54

Data Sampling, Checking and Transformation ............................................................................. 55

Data Sampling ........................................................................................................................... 55

Data Checking ........................................................................................................................... 55

Data Transformation ................................................................................................................. 56

Data Analysis Methods ..................................................................................................................... 57

Unit Root Testing for Stationary Variables .................................................................................. 57

Tests for Cointegration.................................................................................................................. 57

Vector Error Correction Model (VECM) Estimation ................................................................... 58

Impulse-Response and Variance Decomposition Analysis ........................................................... 58

Limitations .................................................................................................................................... 59

5. RESEARCH FINDINGS, ANALYSIS AND DISCUSSION..................... 59

Testing Procedure ............................................................................................................................. 60

Empirical Findings, Analysis and Discussion ................................................................................... 63

Unit Root Testing .......................................................................................................................... 63

Cointegration Testing and VECM Estimation .............................................................................. 64

Tests for Cointegration.............................................................................................................. 64

VECM Estimations ................................................................................................................... 65

IR and VD Analysis ...................................................................................................................... 73

Inspection of the Residuals ....................................................................................................... 73

IR and VD Analysis .................................................................................................................. 74

6. CONCLUSION ......................................................................................... 77

Answers to the Research Questions Posed ....................................................................................... 77

Answers Relating to the Long-Run Dynamics.............................................................................. 77

Answers Relating to the Short-Run Dynamics ............................................................................. 78

Additional Findings .......................................................................................................................... 80

The Effect of the 1994 Elections on the Consumption-Wealth Relationship ............................... 80

The Effect of Volatility in the Data during the 1980s ................................................................... 80

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Key Themes and their Implications on South African Monetary Policy .......................................... 80

Significance of the Concept of an MPC for South Africa ............................................................ 80

Short-Run Consumer Behaviour, Income and Aggregate Wealth in South Africa....................... 81

Using ��� as a Predictor of Consumption Growth in South Africa ............................................. 82

7. FUTURE RESEARCH AREAS ................................................................ 82

8. REFERENCES .......................................................................................... 84

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I. LIST OF FIGURES

Figure 1: A Comparison of the Composition of Household Assets in South Africa between 2005 and

2009 (Source: SARB Quarterly Bulletin, September 2010) .................................................................. 16

Figure 2: Balance Sheet of the Household Sector for Selected Years (R billions) (Source: SARB

Quarterly Bulletin, September 2010) .................................................................................................... 16

Figure 3: Mortgage Debt as a Ratio of Total Household Debt (%) (Seasonally adjusted) (Source:

SARB Quarterly Bulletin, September 2010) .......................................................................................... 17

Figure 4: A comparison of the composition of household debt in South Africa between 2005 and 2009

(Source: SARB Quarterly Bulletin, September 2010) ........................................................................... 17

Figure 5: Household Total Assets, Debt and Net Worth for the Period 2006 to 2009 ......................... 18

Figure 6: Household Total Assets, Debt and Net Worth % YOY change for the Period 2006 to 2009 18

Figure 7: South African Household Net Worth for 2005 – 2010 (% change over four quarters)

(Source: SARB Quarterly Bulletin, September 2010) ........................................................................... 19

Figure 8: Selected Assets of the Household Sector for 2005 – 2010 (% change over four quarters)

(Source: SARB Quarterly Bulletin, September 2010) ........................................................................... 19

Figure 9: Ratio of Household Debt to Disposable Income (%)(Source: SARB Quarterly Bulletin,

September 2010) ................................................................................................................................... 20

Figure 10: Final Consumption Expenditure by Households and Household Wealth (% change over

four quarters) (Source: SARB Quarterly Bulletin, September 2010).................................................... 21

Figure 11: Aggregated Durables, Semi-Durables Non-Durables and Services, Assets and Income for

1975 to 2010 ......................................................................................................................................... 22

Figure 12: Non-Durables and Services, Assets and Income for 1975 to 2010 ..................................... 23

Figure 13: Non-Durables and Services as a Ratio of Aggregate Consumption over the Period ......... 24

Figure 14: Non-Durables and Services, and Aggregate Consumption plotted as ratios of Assets,

Income and Wealth ............................................................................................................................... 25

Figure 15: Effect of Feedback of Data Availability on Variable Selection .......................................... 45

Figure 16: Residuals of the System 1 Variables across the Sub-Sample Period .................................. 74

Figure 17: Impulse Response Analysis of System 1 .............................................................................. 75

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II. LIST OF TABLES

Table 1: Summary of similar empirical studies for eight different economies and various ranges of data ......………………………………………………………………………………………………. 42

Table 2: Comparison of Methodologies of Contemporary Papers ....................................................... 46

Table 3: Measures for Two Systems Generated .................................................................................... 53

Table 4: Sources of Data for Respective Variables .............................................................................. 55

Table 6: Johansen Cointegration Results ............................................................................................. 65

Table 7: Cointegration and VECM Results (for System 1) for a Full-Range Sample, Full-Range Sample including a Dummy Variable at 2005:Q2 and a Long-Range Sub-Sample ............................. 68

Table 8: Cross-comparison of varying Elasticities and MPCs by Economies studied in the Literature ………………. ........................................................................................................................................ 70

Table 9: Variance Decomposition of the Sub-Sample Period for System 1 .......................................... 76

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III. LIST OF ABBREVIATIONS

ADF – Augmented Dickey Fuller

DOLS – Dynamic Ordinary Least Squares

ECM – Error-Correction Model

FPI – Foreign Portfolio Investment

GDP – Gross Domestic Product

IR – Impulse Response

JSE – Johannesburg Stock Exchange

KPSS - Kwiatkowski, Phillips, Schmidt, and Shin

MPC – Marginal Propensity to Consume

OLS – Ordinary Least Squares

PP – Phillips-Perron

SARB – South African Reserve Bank

VAR – Vector Auto-Regression

VD – Variance Decomposition

VECM – Vector Error Correction Model

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IV. ABSTRACT

This study investigates the empirical relationship between household wealth and consumption

in South Africa between 1975 and 2010. A particular focus will be on the long-term trend

parameters, short-run dynamics, and the temporary and permanent effects on this

relationship. The topic under investigation is at the intersection of finance and

macroeconomics, and is of particular importance to emerging countries such as South Africa,

where booming private-sector consumption rates must be managed in light of the importance

of private-sector saving.

A low private saving rate should be a key concern to macroeconomic policy makers for three

reasons. Firstly, a low saving rate may slow down medium-term growth, which is driven by

reinvestment into the economy. Secondly, in addition to slow-growth perpetuation, a low

saving rate makes the economy overly reliant on foreign portfolio investments (FPIs), which

are typically short-term and volatile in nature. Finally, a high household consumption rate

raises aggregate demand, thus increasing inflation rates in the economy.

By dictating the rate at which commercial banks lend money to the South African consumer,

the South African Reserve Bank can control the rate of household consumption, but faces the

risk of unwittingly depressing the economy through mistimed monetary policy interventions.

Thus, there has been recent literature devoted to the construction of appropriate econometric

models that are capable of providing the forecasting power required to implement the desired

aims of monetary policy.

Employing a vector-error correction model (VECM) approach, this paper reaches interesting

conclusions pertaining to the cointegrated relationship between household consumption,

wealth and income in South Africa for the period spanning 1975 to 2010. In the long-run, the

marginal propensities to consume out of wealth and in particular income are high compared

to those of developed economies. The trend residual is found to have predictive power for

income and consumption, as these two variables co-move over quarterly frequencies to adjust

for short-term deviations from the trend relationship binding these three variables in the long

run. The growth in consumption in today’s quarter also predicts next quarter’s change in

income, whilst short-run, temporary movements in asset wealth are largely dissociated with

household consumption. Given South Africa’s social, economic and political legacy, the

reasons for these findings are perhaps unsurprising, yet the findings have far-reaching

implications for South African monetary policy.

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V. ACKNOWLEDGEMENTS

It is with deep gratitude and admiration that mention is made of Mr. S.J. Gossel, whose

character has left an indelible impression on the student. This research has relied heavily on

his expert input; however all remaining errors are with the student.

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VI. PLAGIARISM DECLARATION

1. I know that plagiarism is wrong; it is to use another’s work and pretend that it is my own.

2. I have used the American Psychological Association (APA) convention for all citing and

referencing in this document. Each contribution to, and quotation in this thesis, stemming

from the works of other people, has been attributed to them, and cited and referenced.

3. This thesis is my own work.

4. I have not, and will not allow anyone to copy my work with the intention of passing it off

as her or his own work.

5. I acknowledge that copying someone else’s work or part of it, is wrong, and declare that

this is my own work.

Signature______________________

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For my mother and father

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1. INTRODUCTION

This study investigates the empirical relationship between household wealth and consumption

in South Africa between 1975 and 2010. A particular focus will be on the long-term trend

parameters, short-run dynamics, and the temporary and permanent effects on this

relationship. The topic under investigation is at the intersection of finance and

macroeconomics, and is of particular importance to emerging countries such as South Africa.

Given the sharp increase in domestic housing and equity prices over the last decade in South

Africa, a booming middle-class sector and the country’s re-entry into the global market,

policy makers need to understand how fluctuations in wealth should be responded to,

specifically with regard to interest rate policy, in order to curb consumer spending.

Specifically, monetary policy makers need to know how large the effect of a wealth change is

on private consumption so that, in their bid to control inflation and promote investment-

driven medium- to long-term economic growth, they do not unwittingly depress the economy

through inappropriate interest rate adjustments. As such, a quantifiable measure of the wealth

effect is required.

Based on the landmark work of Ando and Modigliani (1963), economists have used the

following estimation as a rule of thumb: a dollar increase in wealth leads to an increase in

consumer spending of about five cents (Ando and Modigliani, 1963). However the recent

work of Lettau and Ludvigson (Lettau and Ludvigson, 2004) reiterates that only permanent

and not short-term, transitory changes in wealth affect consumption permanently. Finding

that most of the variation in wealth is transitory, Lettau and Ludvigson (2004) stress that an

estimation of the long-term relationship between aggregate wealth and consumption cannot

be used to describe the effects of both long- and short-term movements in wealth on

consumption, as this would result in the wealth effect on consumption being overstated.

Thus in the case of South Africa, if monetary policy makers understand how domestic

consumers react to both permanent and temporary changes in wealth, then they would be

able to make informed decisions when responding to fluctuations in wealth. Studies abroad

have indicated that private consumption in various economies reacts differently to permanent

and temporary variations in household wealth in terms of macro components (i.e. assets and

income), as well as micro components (the financial and non-financial assets of households).

One of the primary objectives of this paper will be to discover how South African consumers

respond to fluctuations in asset and income values respectively.

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In light of the above considerations, this research paper will empirically describe the

relationship between wealth and consumption in South Africa. Before doing so, the following

three subsections provide a context by firstly justifying the relevance of such a study,

secondly reviewing the role of monetary policy in South Africa, and thirdly discussing the

definitions and components of the variables to be investigated in the study and how these

variables have moved over both the last five years as well as over the full period of 1975 to

2010. The argument is concluded by using the evidence provided to justify the development

of an appropriate consumption model which could be used to accurately forecast wealth

effects and implement correct monetary policy interventions for the South African economy.

Government and Private Saving in South Africa

A low private saving rate should be a key concern to macroeconomic policy makers for two

reasons. Firstly, low savings rates may slow down medium-term growth, which is driven by

reinvestment into the economy. Secondly, in addition to slow-growth perpetuation, a low

national savings rate also makes the country reliant on foreign portfolio investments (FPIs),

which are typically short-term and volatile in nature (Aron and Muellbauer, 2000a). The

question may then be raised: How important is household saving in the context of corporate

and government saving? The answer to this question is of paramount importance in weighing

up the significance of an investigation to the relationship between household consumption

and household wealth.

National saving is the sum of all government and private saving, with the latter comprised of

household and corporate saving. Despite the significant contribution of household

consumption to South Africa’s gross domestic product (GDP), previous literature concerned

with household saving in South Africa concluded that within the private sector, increased

corporate savings offset increased dis-savings by households. The literature claims that when

inflation and tax rates increased, corporations would respond by decreasing dividend payouts

(thereby increasing savings), with households rationally increasing consumption as a result of

anticipated increased equity values (Aron and Muellbauer, 2000a). This mechanism,

described as households “piercing the veil” (Barr and Kantor, 1994), in general implies that

the decrease in savings of one entity is completely offset by the other, and as a result, in the

case of the private sector, aggregate saving would remain unchanged. In this way,

understanding the saving behaviour of South African households was considered unimportant

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in forming policies designed to promote saving in line with requirements for economic

growth – only the control of government saving rates was held to be of significance.

However this has subsequently been challenged by Aron and Muellbauer (2000a) who

provide three reasons why, in addition to promoting the government saving rate, promoting

the private saving rate should also form part of South African monetary policy. Firstly, they

argue that the net effect of decreased household savings based on reduced dividend income,

after taking into account increased equity wealth, is non-zero. Secondly, they posit that

corporations could decrease savings even if households pierce the corporate veil. Lastly, they

identify financial liberalisation and lower real interest rates as being capable of changing

relative sectoral saving ratios. All three reasons could ultimately cause increased aggregate

saving or dis-saving in the private sector, as opposed to a zero net-effect. Therefore, since the

individual variation in the contributions of household and corporate saving to aggregate

saving are significant, a thorough understanding of the factors driving household saving, and

thus household consumption, is vital when implementing monetary policy.

The next section deals with monetary policy in South Africa, and will cover three main

aspects: the purpose of monetary policy in South Africa, a brief account of important regime

shifts since the 1960s and a review of the transmission mechanisms which have been

employed by the South African Reserve Bank (SARB) to implement monetary policy. A

special focus will be placed on important omissions in the South African Reserve Bank’s

modelling of the consumption function for South Africa.

Monetary Policy in South Africa

Before conducting the current study, it is useful to build a short context describing the

evolution of monetary policy in South Africa. Post-1995, monetary policy in South Africa

has been tasked with regulating inflation rates and managing currency volatility whilst at the

same time ensuring sufficient economic growth for longer-term political stability (Aron and

Muellbauer, 2000b).1 Since the 1960’s, the South African economy has operated under three

monetary policy regimes, which are discussed briefly as follows.

1 According to the South African Constitution: “The primary objective of the SARB is to protect the value of the

currency in the interest of balanced and sustainable economic growth in the Republic” (Aron and Muellbauer,

2000b, pg.4).

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The regime in place during the 1960s was a “liquid asset ratio-based system” which

employed quantitative controls, with the use of liquid asset requirements being the main form

of monetary control (Aron and Muellbauer, 2000b). Essentially the SARB used a limited

supply of liquid money to control bank loans and the growth of money supply; however this

system was replaced by a “cash reserves-based system” in 1985. Interest rates were then used

to control lending, and in effect the SARB, by setting its interest rate at a relatively high

level, was able to achieve monetary control by creating a “money market shortage”. This also

resulted in commercial bank rates being closely linked to the SARB rate (Aron and

Muellbauer, 2000b).

The current system, termed “repurchase transactions”, was introduced in 1998, where, in

contrast to setting the interest rate, the SARB then “auctioned” money to commercial banks.

Based on an estimated daily liquidity requirement, the market-determined repurchase rate is

that at which commercial banks repurchase money from the SARB, except in the cases of

significant over- and under-provision of liquidity. Inflation targets continue to be announced

and importantly, even with a market-driven repurchase rate system, the commercial bank

interest rate is heavily influenced by the SARB’s preferences for the interest rate level in the

South African economy. Thus, the SARB is still in a position to control the final interest rate

at which a consumer would borrow money from a commercial bank. Such a preference would

depend on the Bank’s inflation as well as South African GDP growth rate targets. Inflation

and investment-driven growth are driven by, amongst other factors, aggregate demand and

private saving respectively, with these last two factors driven heavily by household

consumption. Accordingly, the focus now turns towards the Bank’s modelling of the

consumption function.

Prior to the work of Aron and Muellbauer (2000a), the SARB had provided the most

comprehensive consumption model available for South Africa2. The model incorporated four

separate components of consumption: durables, non-durables, semi-durables and services.

However, the model excluded, amongst other variables, asset values, debt, and proxies for

agents’ expectations, namely future income. Based on most theoretical foundations concerned

with the consumption-wealth relationship, these are significant omissions and until 2003, a

2 Aron and Muellbauer (2000a) construct a consumption function which will be discussed later in this paper.

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comprehensive estimate for the South African household balance sheet3 had not been

constructed. If the personal saving rate, driven by household consumption, and a key

component of aggregate national saving, is considered important enough to be factored into

monetary policy strategies geared towards investment-driven growth, then it can be argued

that it is imperative that an adequate model relating aggregate consumption to total household

wealth be developed. The next section therefore discusses the key components of such a

model.

Household Wealth, Income and Consumption in South Africa

This section is composed of two parts: firstly, a summary of the latest findings of the SARB

regarding household net wealth, disposable income and household consumption, and

secondly, an overview of the long-run movements in household net wealth4, income and

consumption in South Africa, for the period 1975:Q1 to 2010:Q2. Before examining the long-

run developments of each variable (which form the basis of the empirical study to follow), it

is instructive to refer to the findings of the SARB first, in order to attain a better

understanding of the elements that comprise the South African household balance sheet, their

relative proportions, and how the individual variables of household debt, gross assets, income

and consumption have moved relative to each other in recent years.

Based on the pioneering work of Aron and Muellbauer (2006), which developed estimates of

the South African household balance sheet for the period 1975 to 2005 (Aron and

Muellbauer, 2006), the SARB subsequently calculated the estimates for the period 2005:Q1

to 2010:Q2. A note on household wealth (Kuhn, 2010) provided in the SARB’s quarterly

bulletin of September 2010 reports briefly on South African household balance sheet

aggregates, household debt, income, and final household consumption expenditure.

South African household assets have been categorised into two broad categories: tangible (or

non-financial) and financial assets (Figure 1 below). The value of non-financial assets is

given by the market value of residential and non-residential buildings, non-agricultural land,

construction works, machinery and equipment, computers and related equipment, transport

3 This has been estimated by Aron and Muellbauer (2003), and will be discussed later in this paper. The

estimates were first provided to the SARB in 2006; see the SARB Quarterly Bulletin June 2006. 4 In this paper, household wealth is defined as the sum of household net assets and disposable income, and will

also be referred to as “aggregate wealth”. Additionally, household net wealth, the term used by the SARB to

refer to household assets net of household debt, will be referred to simply as “assets”.

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equipment, agricultural land and orchards, and inventories owned by households, not-for-

profit institutions and non-incorporated business enterprises. Financial assets include

monetary assets, pension funds and long-term insurers, equities and bonds and lastly offshore

financial assets (Kuhn, 2010).

Figure 1: A Comparison of the Composition of Household Assets in South Africa between 2005 and 2009 (Source: SARB Quarterly Bulletin, September 2010)

According to Figure 1 above, tangibles comprised about 30% of asset wealth in South Africa

in 2009, slightly larger than the figure estimated for 2005. Figure 2 below presents the

balance sheet for the period 2005 to 2009 with estimates made on an annual frequency. Four

important figures listed are: total assets, total household debt, household net worth and net

worth including consumer durables. Household net worth, given as total assets net of debt,

increased by almost 42% between 2009 and 2005, with household debt increasing by

approximately 70% over the same period.

Figure 2: Balance Sheet of the Household Sector for Selected Years (R billions) (Source: SARB Quarterly Bulletin, September 2010)

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As in the case of total asset wealth, household debt is measured across the following entities:

private households, non-incorporated businesses and not-for-profit institutions. Mortgage

advances to households and consumer credit are the two categories of household debt, with

the share of mortgage debt in total household debt increasing from almost 57% in 2005 to

roughly 64% in 2009 (Figure 3). Consumer credit is comprised of instalment sales and

leasing finance, open accounts, securitisation transactions, personal loans, debt with local

authorities and non-incorporated credit (Figure 4).

Figure 3: Mortgage Debt as a Ratio of Total Household Debt (%) (Seasonally adjusted) (Source:

SARB Quarterly Bulletin, September 2010)

Figure 4: A comparison of the composition of household debt in South Africa between 2005 and 2009 (Source: SARB Quarterly Bulletin, September 2010)

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The net wealth of the household sector increased noticeably from the first quarter of 2003 up

to the second quarter of 2008, largely reflecting the sharp appreciation in the value of

residential property and the surge in equity prices (Kuhn, 2010, pg. 70). Subsequent to this

period however, the global financial crisis resulted in year-on-year decreasing values for total

household assets and net worth between 2007 and 2008, driven by declines in both property

and equity prices (Figures 5 and 6).

Figure 5: Household Total Assets, Debt and Net Worth for the Period 2006 to 2009

Figure 6: Household Total Assets, Debt and Net Worth % YOY change for the Period 2006 to 2009

0

1000

2000

3000

4000

5000

6000

7000

2006 2007 2008 2009

Total assets (R'bn)

Net worth (R'bn)

Total debt (R'bn)

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

2006 2007 2008 2009

Total assets (% YOY

change)

Net worth (% YOY change)

Total debt (% YOY change)

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As indicated by Figure 7, household net worth has since the 2nd quarter of 2009 recovered

reasonably well as a result of steady increased house prices since the middle of that year, as

well as through increases in the total value of equities (see Figure 8 below). It is of further

interest to note from Figure 6 that the year-on-year change in household debt remained

positive throughout that period of volatility.

Figure 7: South African Household Net Worth for 2005 – 2010 (% change over four quarters) (Source: SARB Quarterly Bulletin, September 2010)

Figure 8: Selected Assets of the Household Sector for 2005 – 2010 (% change over four quarters) (Source: SARB Quarterly Bulletin, September 2010)

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Given this positive year-on-year change over the period, household debt rose steadily

between 2005 and 2009. For the period between 2005 and 2007 this increase was driven

mainly by rapidly rising residential property prices (Kuhn, 2010). According to Kuhn (2010),

the following three factors may have sustained the accumulation of debt over the period of

2005 - 2008: a relatively low interest rate environment, easier access to credit and an

increasing number of people in paid employment. The proportion of household debt to

disposable income reached a record figure of 82 per cent in the first quarter of 2008 (Kuhn,

2010). However, by the end of 2008, growth in disposable income slowed as households

experienced financial strain, driven by poor economic conditions in light of the global

downturn which led to an increase in unemployment (Kuhn, 2010). The rate of increase in

household debt, though positive, also slowed down for the period, thus leading to the first

decline in the household debt to disposable income ratio since the first quarter of 2008

(Figure 9).

Figure 9: Ratio of Household Debt to Disposable Income (%)(Source: SARB Quarterly Bulletin, September 2010)

Despite this recent slowdown, household debt (a primary transmission mechanism of a

wealth effect) increased by almost 20 per cent over the period 2005 to 2010. However, the

proportion of household debt to disposable income in South Africa is still lower than that of

economies such as the United States, England, Australia and New Zealand (Kuhn, 2010).

Given this slowdown in debt accumulation, Figure 10 shows decreasing quarterly growth in

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nominal household consumption between mid-2007 and mid-2009, with a steady recovery

following increased household net wealth over the next four quarters.

Figure 10: Final Consumption Expenditure by Households and Household Wealth (% change over four quarters) (Source: SARB Quarterly Bulletin, September 2010)

Having considered the role of household debt, the discussion now turns to an overview of the

movements in household consumption (from now on referred to as consumption), household

net wealth (from now on referred to as assets), and household income (from now on referred

to as income), for the period 1975 to 2010. With regard to South Africa, the SARB provides a

measure of total household consumption, and also lists four sub-categories which decompose

the aggregate figure: durables, semi-durables, non-durables, and services. This paper groups

non-durables and services into one measure for consumption, with the sum of all four sub-

categories as another; it is important to bear in mind that the latter (from now referred to as

aggregate consumption) does not represent theoretical total consumption, and that both

measures are simply proxies for total theoretical household consumption5. As opposed to

after-tax labour income, the measure provided by the SARB for income is personal

disposable income. On its website6, the SARB has provided a ratio relating nominal assets

(household net worth) to nominal income, from which the asset figure per quarter can be

5 A more detailed discussion of this matter, as well as the associated nomenclature follows later. 6 www.reservebank.co.za

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calculated. Figure 11 shows the movements of aggregate consumption, assets and income in

South Africa for the period 1975 to 2010.

Figure 11: Aggregated Durables, Semi-Durables Non-Durables and Services, Assets and Income for 1975 to 2010

Figure 11 demonstrates how all three variables appear to move together in the long run

(specifically between 1975 and 2003), but not necessarily over short-run periods.

Furthermore, closer inspection of the graph shows that assets are extremely volatile, even

over quarterly frequencies, with aggregate consumption and income perhaps exhibiting more

stable, predictable behaviour. Confirming the previous discussion, Figure 11 shows the rapid

rise in the market value of assets in 2003 which coincided with a housing boom as well a

sharp rise in stock market wealth. In the midst of this wealth boom income responded

sharply, more so than aggregate consumption, such that personal income approximately

equalled aggregate consumption in the third quarter of 2005. Income and aggregate

consumption also responded with different lags and magnitudes in response to both the burst

of the wealth bubble in 2007 as well as the economic recovery in 2009, with the result that

the two variables have been negatively correlated with each other over a few sub-periods

during the last seven years.

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

1975 1980 1985 1990 1995 2000 2005 2010

Aggregate consumption (R'm)Assets (R'm)Income (R'm)

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Figure 12: Non-Durables and Services, Assets and Income for 1975 to 2010

Further to this discussion regarding the relative movements of consumption and income,

Figure 12 shows that across the full period of 1975 to 2010, income co-moves with the

consumption of services and non-durables. It is also evident that this measure of consumption

responded faster than the aggregate measure in the period between 2003 and 2010, when the

value of assets varied significantly. Figure 13 shows that the proportion of non-durables and

services in aggregate consumption has increased steadily over the full period, reaching a peak

of almost 83% in the third quarter of 2009. Therefore, non-durables and services have been

more strongly correlated with income than aggregate consumption, and one may infer from

the data that slow responses in aggregate consumption, particularly over the last seven years,

may be attributed to a decreasing rate in the increase in consumption of durable and semi-

durable goods. Apart from the fact that the growth of the consumption of durables and semi-

durables has been less than that of services and non-durables, in general, it makes intuitive

sense that in response to an increase in total wealth, the consumption of services and non-

durables should respond faster than that of durables and semi-durables, since consumption of

services and non-durables relates more to a “flow”, which possibly facilitates a faster

response time than that of aggregate consumption, which also takes into account the

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

1975 1980 1985 1990 1995 2000 2005 2010

Services and non-durables (R'm)Assets (R'm)Income (R'm)

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intermittent replacement of stock items related to the consumption of durables and semi-

durables (Lettau and Ludvigson, 2004).

Figure 13: Non-Durables and Services as a Ratio of Aggregate Consumption over the Period

Figure 14 plots both measures of consumption separately as ratios of assets, income and

wealth respectively, with wealth defined as the sum of existing assets (household net worth)

and expectations of future financial reward (income). The ratios show that over the full

period, there has been a greater increase in the consumption of services and non-durables

than in income, whilst the long-term increase in income has exceeded that of aggregate

consumption. This does not mean that there is a negative correlation between income and

aggregate consumption, but rather that income has increased more than aggregate

consumption over the full period, but less than the consumption of services and non-durables.

.50

.55

.60

.65

.70

.75

.80

.85

1975 1980 1985 1990 1995 2000 2005 2010

Ratio of services and non-durables to aggregate consumption

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Figure 14: Non-Durables and Services, and Aggregate Consumption plotted as ratios of Assets, Income and Wealth

The evidence provided in the overview above suggests a long-run relationship between

consumption, assets and income for South African data, particularly over the period of 1975

to 2003. Following this period, whilst not proven yet, there does appear to be a break in this

long-run relationship; however if this is the case then one may postulate with confidence that

this break may be due to the wealth bubble7 towards the end of the period, rather than a break

in the underlying relationship between the three variables. If the latter is the case, then one

may anticipate with similar confidence a correction in the economy, which would restore the

system back to its long-run relationship. This should be of key concern to monetary policy-

makers, but since policies are monitored over periods much smaller than the above, an

understanding of the short-run interplay between the three variables is also necessary.

Over the short-term, the data appears to suggest that there is significant interplay between the

variables, as well as non-responses in certain variables to volatile, seemingly temporary 7 According to Kuhn (2010), South Africa, as in the case of many other countries, was experiencing an asset

price bubble during the years of 2003-2008.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1975 1980 1985 1990 1995 2000 2005 2010

Ratio of non-durables and services to assetsRatio of aggregate consumption to assetsRatio of non-durables and services to incomeRatio of aggregate consumption to incomeRatio of non-durables and services to wealthRatio of aggregate consumption to wealth

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changes in others. This is a crucial point because if monetary policy makers were better

informed about the short-run responses of consumption to short-run deviations in assets and

income, the long-run relationship between all three variables and even changes in

consumption itself in the previous quarter, then it is possible that interest rate adjustments

may be better informed. Furthermore, another key piece of information which policy makers

would require would be the time-duration of the innovations of one variable on another.

Policy makers would then know how long it would take for the effect of that variation to

“wear off” in the economy. These long- and short-run effects may only be computed with a

proper model for consumption.

If the household consumption rate is deemed important to GDP growth and inflation rate

targets, then it is imperative that the consumption function is understood in terms of the South

African household sector’s response to the variation in aggregate wealth in the economy,

which is comprised of assets and income. This is substantiated by the evidence above, which

demonstrates that the three variables are intertwined. Instead of adjusting interest rates today

based on the measurement of last quarter’s household consumption, it makes more sense to

forecast consumption for the next quarter and apply appropriate interest rate modifications

today, taking into account that such modifications would in themselves only influence the

macroeconomy after a certain period. An increase in the interest rate would serve to cool

inflation, but the transmission would require a period of time to have an impact and thus

could actually create negative effects if mistimed. Thus, there has been recent literature

devoted to the construction of appropriate econometric models that are capable of describing

the relationships above and providing the forecasting power required to implement the

desired aims of monetary policy. However, before the literature is reviewed, a set of discrete,

mutually exclusive questions is needed to translate the discussion above into econometric

terms that can be empirically investigated.

2. RESEARCH QUESTIONS AND SCOPE

Research Question and Sub-Questions:

This paper seeks to answer the following primary question: How large is the wealth effect for

South Africa, given data over the period of 1975:Q1 to 2010:Q2? In addition, the following

set of secondary questions relating to the long-run and short-run dynamics also arise:

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Sub-Questions Relating to the Long-Run Dynamics:

1. Do the variables of consumption, assets and income have one or more cointegrated

relationships?

2. What are the respective shares of income and assets in total wealth in South Africa?

3. How can the long-run response of household consumption in South Africa be described

(what are the marginal propensities to consume out of assets and income respectively and

how do these MPCs compare with those of developed economies such as the USA,

Canada, England, Germany, Sweden, Australia and New Zealand)?

4. Have there been wealth bubbles that have structurally broken the long-run relationship

between household consumption and wealth; and if so, is there evidence of a breakdown

in the cointegrated relationship across the full sample of data to support this?

Sub-Questions Relating to the Short-Run Dynamics:

1. How do the short-run movements in the long-run relationship influence each of

consumption, assets, and income and which variable contributes most to the long-term

correction?

2. How does each variable respond to temporary changes in the other variables in the

previous quarter, including that of its own?

3. How do these short-run dynamics compare with those of developed economies (such as

the USA, Canada, England, Germany, Sweden, Australia and New Zealand)?

4. What proportion of the variance in each variable is attributable to the influence of each of

the other variables?

5. What is the duration of the shock, and thus influence, of one variable on another?

Research Assumptions

It is assumed that:

1. The data for the research is of a generally acceptable standard that will allow correct

application of the economic theory, econometric model, and econometric estimation

techniques to produce the most accurate reflection of the consumption-wealth relationship

for South Africa, for the periods under question.

2. The underlying economic theory to be used (the permanent income hypothesis and life-

cycle model) represents our best understanding of modelling consumption.

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3. The model and estimation techniques are sufficiently robust when applied to a developing

economy since most of the studies conducted to date are for developed economies.

4. The data used for the study are taken with the South African economy operating under

steady-state conditions.

The remainder of this paper is organised as follows: Section 3, adopting an outside-in

approach, provides a review of the theoretical and empirical literature related to the topic.

Section 4 describes a methodology for the focused, applied research to be conducted where

special attention will be placed on model selection, testing methods, variable selection and

data selection and processing. Section 5 presents the steps followed in developing the

empirical findings of the study, an analysis of the empirical results and a discussion linking

the analysis to the secondary questions developed above. Section 6 provides an answer to the

over-arching primary question posed by the research topic, lists additional findings, and

discusses implications of the research on monetary policy in South Africa. Section 7 closes

the paper with a discussion of future research directions.

3. LITERATURE REVIEW

Discussion

This literature review is divided into five sub-sections. The first sub-section provides the

reader with a general overview of the basic, underlying theory which forms the basis of any

research into the consumption-wealth relationship. It is not intended to be comprehensive,

and the underlying theory is not evaluated; it is merely presented to provide a context and the

most fundamental starting point for the remainder of the research to be undertaken. It is from

the second sub-section of the literature review that the paper makes its first detour. The life-

cycle model is chosen as the foundation for the econometric analysis to follow, justified on

the basis that most investigations into the consumption-wealth relationship use the life-cycle

model as their econometric foundation.

Having covered a basic overview of the general theory, the third and fourth sub-sections deal

specifically with some of the more important factors which determine the individual effects

of housing and financial wealth on consumption respectively. The justification for including

these sub-sections in the literature review is that the information provided in these sections

will allow for easier interpretation of the results of the econometric analysis to follow in the

main report, as well as point the researcher in the direction of fair hypotheses prior to

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carrying out the main analysis. In the case of South Africa, factors such as deep socio-

economic inequality as well as its housing and financial market regulations could be expected

to significantly affect the transmission of wealth fluctuations onto consumption. Additionally

the recent housing price boom and large increase in equity prices may have generated “wealth

bubbles” that significantly influenced the wealth-consumption relationship in the last decade.

Therefore, whilst household asset worth has not been disaggregated into its financial and non-

financial (comprised mainly of residential property wealth as detailed in Section 1)

components8, understanding the dynamics of the transmissions mechanisms of variations in

the disaggregated forms of household assets onto consumption can assist the researcher in

interpreting the analysis of the effects of the aggregated variable.

The fifth sub-section of the literature review focuses on the empirical literature, but departs

along a specific strain found within contemporary studies. Instead of presenting the findings

of general consumption-wealth relationship studies, the works of Ludvigson and Steindel

(1999), Lettau and Ludvigson (2001), and Lettau and Ludvigson (2004) are considered in

more detail. The aim will be to demonstrate the progression of thought within the literature in

recent years, illustrate the gaps in the literature, and then justify why the rest of this research

report will adopt a particular empirical approach as opposed to the alternatives. Following

that, the more recent literature based on the landmark findings of Lettau and Ludvigson

(2004) will be reviewed. These latest studies have contributed to the field in a significant

way, and the remainder of this research report, as an applied study, aims to replicate the

methodologies used by these authors, and apply them to study the relationship between

wealth and consumption in South Africa. Finally, the empirical study conducted for South

Africa by Aron and Muellbauer (2000a), will be briefly reviewed.

Modelling Consumption – The Underlying Theory

Contemporary studies that investigate the relationship between wealth and consumption tend

to depart immediately from the life-cycle-model as proposed by Ando and Modigliani (1963).

This current study follows from the work of Cutler (2005) which illustrates two basic

approaches, each stemming from the ‘permanent income hypothesis’, to modelling the

wealth-consumption relationship.

8 The SARB has not disclosed the disaggregated estimates of household net wealth, or assets, to the public.

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A standard approach to modelling consumption assumes that consumers aim to maximize the

present value of the sum of utilities of consumption in each future period (Cutler, 2005, pg.

218). This maximum value is given by:

�����∑ �� + �������� �������. (1)

The above expression is subject to an intertemporal budget constraint which states that the

difference between labour income and consumption is accumulated assets . This is given as:

���� = �� + ������ − �� −��� (2)

Where U’ is the first derivative of a concave one-period utility function, Ct is consumption,

δ is the subjective rate of time preference, ���� is the end-period net housing and financial

wealth, �� is labour income, and �� is the real interest rate. According to Cutler (2005), there

are two approaches to solving the above optimisation problem and these will be covered

briefly in the next section.

The Optimal Consumption Path and the Life-Cycle Model

Optimal Consumption Path

The description of the optimal consumption path that follows in this section is based on

Cutler (2005, pg. 218). An Euler equation or first-order condition can be generated, in order

to describe the optimal consumption path of a representative consumer who can borrow and

lend at the risk-free rate:

�������� = ���� ! ���������"�

�����# (3)

In the above equation, the consumer should, under optimum conditions, be unable to increase

his/her expected lifetime utility by reducing consumption by one unit and increasing his/her

assets, and consuming the extra gross returns the next period (Cutler, 2005, pg. 218).

Assuming that preferences are quadratic and the real interest rate is constant and equal to the

subjective rate of time preference, the growth of aggregate consumption follows a random

walk. Known as the Hall equation, this is shown as:

∆�� =∝ +&� (4)

In the above equation the change in consumption is given by the sum of a constant ' and &t is

the revision between the current period and that of one period before, of the individual’s

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assessment of his/her permanent income. The essence of the Hall model above is that as

permanent changes in income are unpredictable, so is consumption for the next period not

possible to forecast, i.e. it follows a “random walk9” (Koop, 2009). This is in contrast to the

life-cycle model below, which considers consumption as a function of total wealth,

forecastable by changes in current wealth.

Life-cycle Model

The life-cycle theory of Modigliani (1963) has frequently been used to facilitate accurate

modelling of economic data. Thus, the rest of this paper will be based largely upon the theory

underlying the life-cycle model. The life-cycle model explains consumption as a variable

dependent on wealth (Barata and Pacheco, 2003):

��∗ = )�����,+�� (5)

The equation above states that household planned consumption ,-∗ is a function of total

resources, which are net asset wealth at the start of the period (.-�/� and human wealth (0-�. The core thesis of the “life-cycle theory” is that households will ‘smooth’ out their

consumption in the face of uneven wealth and income streams. In other words, future

consumption, or the change in consumption between current and future levels, may be

affected by changes in wealth.

Since human wealth is itself not directly observable, labour income is used as a proxy, and

therefore the effect of wealth on consumption has traditionally been measured by estimating

aggregate time-series regressions of the form (Ludvigson and Steindel, 1999):

�� = � + 1.�� + 2. �3� +4� (6)

In equation (6), YP is a measure of permanent income, W is consumer net worth as measured

at the beginning of the period, et is an error term capturing other factors that influence

consumption while b and c represent the marginal propensities to consume (MPC) out of

wealth and disposable income respectively.

A rule of thumb is that b is on the order of 0.05 (Ludvigson and Steindel, 1999), i.e. a dollar

increase in wealth leads to an increase in consumer spending of roughly five cents. Equation

(6), although providing the basis of current empirical work, tends to suffer from theoretical

9 Where �� =∝ +���� + &�

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criticisms as well as econometric problems, which will be taken up later in this literature

review.

Equation (6) may be expanded further by disaggregating wealth into its financial and non-

financial components, or net non-housing wealth (At) and net housing wealth (Ht)

respectively, thus obtaining:

�� = � + 2�. �� + 25. 5� + 2+. +� +4� (7)

In equation 7, �6, �7 and �8 are the MPC parameters of Y, A and H respectively (Chen, 2006).

Disaggregation of total wealth into financial and housing wealth is necessary in order to note

their individual effects on consumer spending.

Effects of Stock Market Wealth on Consumption

In the case of the United States it has been that the effect of variation in stock market wealth

may have strengthened over time with the broadening of equity ownership (Poterba,

Samwick, Shleifer, and Shiller, 1995). Hence, although the percentage of households with

direct equity ownership has been declining, there has been an increase in indirect holdings

through mutual funds, private and public pension plans, personal trusts etc, which allows for

more individual investors to be exposed to the variations in the stock exchange. However

Poterba (2000) argues that since much of the total amount of stocks in the United States are

owned by a small number of families, the impact of variations in stock market wealth will

have a small, if not negligible effect, on aggregate consumer spending (Poterba, 2000).

The effect of stock market wealth on consumption is therefore an ongoing topic of debate,

since a skewed concentration of stock holdings may imply that swings in stock market wealth

have little effect on aggregate consumer spending (Barata and Pacheco, 2003). In the case of

a society with deep socio-economic inequality, such as that of South Africa’s, where stock

market holdings are concentrated in a small subset of the population irrespective of whether

the holdings are direct or indirect, it may be justifiably hypothesised that swings in the total

value of equities will have trivial effects on aggregate household consumption, which should

reflect the value of consumption made up by the total population.

Consumer behaviour can also be affected via stock market wealth, where the prices of

equities are viewed as leading indicators of cyclical developments in the economy, as well by

the effect that increases/decreases in the stock market have on consumer confidence (Akin,

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2008). As an example, at the onset of the Great Depression in 1929, the uncertainty following

the crash caused a delay in consumer spending due to low consumer confidence (Romer,

1990). Therefore, as pointed out by Akin (2008), even a household that is not invested in the

stock market may have its consumption behaviour altered as stock market wealth varies over

time.

In addition, the removal of barriers to cross-border investment means that fluctuations in

foreign stock prices and international capital flows are having increased impacts on domestic

markets. This increased integration of world capital markets has induced contagion and co-

movements of stock markets across the world and consequently, the effects of international

economic conditions are relevant to consumer behaviour (Dornbusch, Chul, and Stijn, 2000).

The focus now moves on to the effects of variations in the value of tangible assets owned by

the household, which is made up mainly by the market value of residential property.

Effects of Housing Wealth on Consumption

Referring back to the permanent income hypothesis, academics have attempted to understand

the transmission mechanism from variations in residential wealth to changes in consumption.

It is reasonably intuitive that with a residential price increase, there should be a

corresponding increase in consumption, as homeowners feel wealthier and are thus more

willing to save less, and spend more (Chen, 2006). Since houses can be used as collateral to

extend credit for the purchase of consumable goods, the ‘credit channel’ is a link noted by the

literature which relates changes in house prices to fluctuations in consumption. Iacoviello

(2004) develops a model showing how increasing house prices lead to increased borrowing

capacity thereby stimulating increased consumption (Iacoviello, 2004). Theoretical and

empirical studies have however demonstrated that this simple intuition belies the difficulties

encountered in this transmission mechanism from an increase in wealth to an increase in

consumption.

Hindrances to liquidation of newly acquired housing wealth, suspicion of the permanency of

increased house prices, and the viewing of housing assets as long-term savings also inhibit

the transmission of possible housing wealth effects onto consumption (Chen, 2006). Using

U.S. micro data, Engelhardt (1996) found that losses rather than gains in housing prices

affected consumer spending of homeowners (Engelhardt, 1996). Two possible reasons are

suggested: possible hindrances to liquidate the housing capital gain, and a degree of suspicion

regarding the permanency of the increase in housing prices. Additionally, households may

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have an intergenerational ‘bequest motive’ which incentivises homeowners away from

reacting to increases in housing prices. This psychology seems to suggest that houses are

viewed as assets used as vehicles for long-term savings, whereas assets such as stocks are

used by homeowners for more current expenditures (Case, Quigley, and Shiller, 2005).

The distribution of housing wealth within an economy also plays a significant role. In

contrast to stock market wealth, housing wealth is generally spread more evenly over a

population and therefore might have a larger impact on consumption if changes in property

prices are seen as permanent (Akin, 2008). However in the case of South Africa, ownership

of tangible assets (which comprise almost 30% of household net worth) is deeply skewed, as

the bulk of South Africans live in poor conditions. Thus, in the absence of hindrances, even if

increases in property prices are viewed as permanent, it may be hypothesised with confidence

that increases in residential values will not transmit significantly onto aggregate consumption.

Having reviewed the theoretical literature pertaining to the topic, from both the classical

economic perspective as well as that of the more practical considerations pertaining to

financial and non-financial (tangible/residential) wealth, the next section reviews the

empirical literature concerned with the relationship between wealth and consumption.

Review of the Empirical Literature

The focus of this literature review now departs along a specific strain found within

contemporary studies. Instead of presenting the findings of general consumption-wealth

relationship studies, the works of Ludvigson and Steindel (1999), Lettau and Ludvigson

(2001), and Lettau and Ludvigson (2004) are considered in more detail. The aim here will be

to demonstrate the progression of thought within the literature, illustrate the gaps in the

literature, and then justify why the rest of this research report will adopt a particular empirical

approach as opposed to the alternatives.

Ludvigson and Steindel (1999)

Based on the large movements in the U.S. stock market in the second half of the 1990’s,

Ludvigson and Steindel (1999) conducted research to determine the stock market effect on

household consumption, from 1952:Q4 to 1997:Q4. In performing the analysis, the study

used two techniques. The first technique, based on the traditional ordinary least squares

(OLS) specification function, illustrated the short- and long-run relationship in a single

equation and was carried out essentially to serve as a basis for comparison with earlier

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studies. Thereafter, a technique was employed which first used a dynamic ordinary least

squares (DOLS) analysis to estimate the long-run relationship between consumption, wealth

and income, and thereafter a restricted vector autoregression (VAR) analysis to estimate the

short-run dynamics. The model used to conduct the traditional OLS analysis is as follows:

�� = ∑ �9���9:9�� + ∑ ;9<���9

:9�� + ∑ μ9>���9

:9�� + 4� (8)

In equation (8), SW and NW refer to stock market and non-stock market wealth respectively,

and i = lag length. Estimates of the above model were performed over a long-run full sample

and three subsamples. However, the analysis produced unstable results which demonstrated

that the OLS estimation of the traditional life-cycle model suffers from two shortcomings:

(1) although each of the variables consumption, wealth and income were likely to have

contained a stochastic trend component, the OLS analysis does not consider that the variables

could have been non-stationary, and (2) the model does not cater for ‘endogeneity bias’

(arising from ‘reverse-causality’ since focusing only on the effect of wealth on consumption,

one would ignore the reverse effect of the effect of changes in consumption on wealth). As a

result, Ludvigson and Steindel (1999, pg. 35) derive an alternate empirical approach based on

the permanent income hypothesis (Ando and Modigliani, 1963) to address both problems.

As previously noted, according to this theory, consumption of nondurable goods and services

is set to be proportional to permanent income. The OLS model thus implies that consumption

responds to any unpredictable change in permanent income, but very little to transitory

fluctuations in income. Additionally, there are no lags in the adjustment of consumption to an

unexpected change in permanent income. This assumption implies that next period’s change

(or growth) in consumption should be unforecastable given information today, which can be

represented as:

�� = ' + ?�� + ��� + @� (9)

Where the error term, A- takes the form:

@� = ∑ B9C9�� ���∆���9 − D� (10)

In equation (10), E-is the expectation operator conditional on information available at time t,

F is the mean change in labour income, and G is a positive constant less than one. In equation

(9), H and I, referred to as the marginal propensities to consume (MPC) out of wealth and

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income respectively, give the effect of a one-dollar increase in wealth and labour income on

consumption.

The aim of equations (9) and (10) is to compute the MPCs β and δ. However, empirically it is

first necessary to determine if the variables of consumption, wealth and income are

cointegrated since cointegration of the variables will eliminate the problem of regressor

endogeneity and also make the empirical approach robust to omission of variables in the

model that could explain the consumption-wealth link. The cointegrating vector is given as

[1, -β, -δ], and therefore one may interpret the MPCs as those parameters which keep

consumption, wealth and income linked to a common trend, or linked over the long-term.

Employing a dynamic ordinary least squares (DOLS) estimate developed by Stock and

Watson (1993), Ludvigson and Steindel eliminate the effects of regressor endogeneity on the

distribution of the least squares estimator and thus compute consistent point estimates of the

MPCs. The DOLS application of equation (9) takes the following form (Stock and Watson,

1993):

�� = ' + ?�� + ��� + ∑ ?9:9��: ∆���9 + ∑ �9

:9��: ∆���9 + @�

∗ (11)

Where ∆ is the first-difference operator and u*t is related to ut such that:

@�∗ = @� −∑ ?9

:9��: ∆���9 − ∑ �9

:9��: ∆���9 (12)

Equation (11) is specified to estimate only the long-term, or trend relationship that links

consumption, labour income and wealth, whereas equation (7) models both the long- and

short-run parameters of the relationship, i.e. the trend parameters and the adjustment process

of consumer spending to disturbances from the equilibrium path10. Since the estimation of

equation (11) separates the long- and short-run components, it is anticipated that this equation

will produce more robust estimates of the trend component. Furthermore, in order to

determine the short-run dynamics of the system, Ludvigson and Steindel (1999) employ a

restricted vector autoregression (VAR) model with the following form (Ludvigson and

Steindel, 1999, pg. 39):

∆�� = D + 'J2��� − ?KLM��� − �KLN���O + ∑ PQ:Q�� ∆���Q + 4� (13)

10 As will be pointed out later, the assumption that it is only consumption that adjusts to restore the equilibrium

is weak, which lays the foundation for the use of more sophisticated techniques to properly understand the

consumption-wealth relationship.

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Where is ∆R- is the vector of log first differences, �∆�-, ∆S- , ∆�-�′ and the parameters HUV and

IUV are the previously estimated cointegrating coefficients for ct, wt and yt. The parameters F,

W and X govern the short-term dynamics - that is, the relationship of consumption, wealth,

and labour income growth as well as the lags of these variables and the trend deviation in the

second term; the parameters in this second term are the estimated coefficients from the DOLS

procedure.

Using U.S. data from 1952:Q4 to 1997:Q4, Ludvigson and Steindel (1999) estimated the

cointegrating relationship between consumption, wealth and income and investigated the

short-run dynamics of the system, in order to determine the stock market effect on

consumption. Catering for instability in their analysis, their main findings were that

movements in the U.S. stock market influences consumption contemporaneously, and not that

of a quarter or more forward. However, they did not investigate the permanent and transitory

components of changes in wealth, the quantitative importance of these components, and their

implications on consumption. Following on this work, Lettau and Ludvigson (2001) were

able to exploit the cointegrated relationship of consumption, assets and income, and use the

residual from a DOLS analysis to forecast future changes in wealth.

Lettau and Ludvigson (2001)

Lettau and Ludvigson (2001) expand on the theoretical framework of Ludvigson and

Steindel (1999) in order to determine the parameters of the shared trend of consumption,

wealth and income for the United States using data from 1952:Q4 to 1998:Q3, before going

on to use residuals of the ���Y variable to predict excess stock returns. Using a DOLS

approach to compute the long-run residual, or trend deviation, Lettau and Ludvigson (2001)

then demonstrate that these fluctuations in the consumption-wealth ratio can be used to

predict both real stock returns and excess returns over a Treasury bill rate, and that this

variable is a better forecaster of future returns at short and intermediate horizons than the

dividend yield, dividend payout ratio, and many other common forecasting variables.

However, as is the case with the Ludvigson and Steindel (1999), the study of Lettau and

Ludvigson (2001) has three shortcomings: first, the permanent and transitory elements of

wealth are not formally identified; second, the relative quantitative importance of the

permanent and transitory elements of wealth are not documented; and third, the

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corresponding implications on consumption as a result of the permanent and transitory

components are not explored.

Lettau and Ludvigson (2004)

The traditional approach used to empirically estimate the association between household

wealth and consumption was the Engel-Granger single equation error correction (ECM)

model (Engle and Granger, 1987). However, Lettau and Ludvigson (2004) argue that this

approach incorrectly assumes that changes in wealth can be treated as exogenous, with the

implicit assumption that following a change in wealth, it is only consumption that will

perform all the adjustments to revert the system back to the new long-term equilibrium while

wealth and labour do not adjust (Chen, 2006). Therefore the coefficients of a short-run ECM

would overstate the wealth effect on consumption. In contrast, Lettau and Ludvigson (2004)

used a vector error correction model (VECM) and found that the adjustments to the

disequilibrium are made by total asset wealth and not consumption. The generalised VECM

is given as:

∆�� = Z + ['\����� + P�]�^���� + 4� (14)

Where ∆�� is a vector containing the differences in the log level of ��, Z is a (3 x 1) vector of

constant terms, [ is a (3 x 1) vector of adjustment coefficients describing which component

of ∆�� responds to the residual term '\����� (with '\� the vector of cointegration) saved from

the DOLS estimation, and _�]� a vector of coefficients describing the lagged effect of `����

on ∆��.

Lettau and Ludvigson (2004) therefore argue that understanding the wealth effect on

consumption requires a systems approach, whereby both consumption and wealth are allowed

to behave endogenously, rather than a single equation modelling approach (Fisher, Otto, and

Voss, 2009). In addition, a VECM is better able to take into account the dynamic responses

of all variables in a cointegrated system and thus obtain more robust parameter estimates of

the link between wealth and consumption (Chen, 2006).

Using the VECM approach and incorporating impulse response and variance decomposition

(IR and VD) analysis, Lettau and Ludvigson were then able to separate the variation in

wealth into its permanent and transitory components. The results show that most of the

variation of wealth was transitory in nature, driven mainly by fluctuations in the stock

market. In contrast, the transitory component elicited little or no response in consumption

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whereas permanent shocks had real long-term effects. These results have important

implications for policy since in an effort to curb consumer spending (and therefore inflation),

monetary policy makers may increase interest rates in light of increasing asset wealth, when

such increases may only be of a transitory nature and thus the decision to curb consumption

at that point in time may be incorrect.

Although Lettau and Ludvigson (2004) shed new light on modelling and understanding the

transitory and permanent components associated with the wealth-consumption relationship,

Chen (2006) notes that the study could be further developed by taking the following four key

aspects into account: Firstly, disaggregating net wealth into its financial and non-financial

(residential property value along with other tangibles) components; secondly, investigating

whether consumption, income, housing wealth and financial wealth are cointegrated; thirdly,

determining which component of wealth contributed most to the long-term equilibrium

correction; and lastly, showing the relative importance of housing wealth and financial wealth

on the movement of consumption, both in the long- and short run.

Literature Based on Lettau and Ludvigson (2004)

Other studies that have used the VECM approach to study the trend and cyclical relationships

between consumption, wealth and income, as well as impulse response and variance

decomposition to split the variation in wealth into its permanent and transitory components,

include those for Australia (Fisher, Otto, and Voss, 2009), Canada (Pichette and Tremblay,

2003), Germany (Hamburg, Hoffmann, and Keller, 2008), New Zealand (De Veirman and

Dunstan, 2010), Sweden (Chen, 2006) and the United Kingdom (Fernandez-Corugedo, Price,

and Blake, 2007). Table 1 below presents a general summary of these papers and also

includes Lettau and Ludvigson (2004) as a reference paper.

Existing Empirical Studies for South Africa

Aron and Muellbauer (2000a) present two models for estimating both the personal savings

rate as well as the corporate savings rate for South African data spanning 1970 – 1998. They

compile the savings ratio as a function of consumption, with the latter modelled according to

Equation 5 above. The consumption function is then written out in a log-linearization of

Equation 5, thereby creating a linear equation relating consumption to assets and expected

income. In order to solve the resultant model, Aron and Muellbauer (2000a) then construct an

estimate (albeit incomplete at the time) of the value of personal assets for South African

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households as well as a forecast of the growth rate of personal disposable income in South

Africa. Accordingly, they were able to produce an estimate of the personal saving rate in

South Africa. One of their key steps was accounting for financial liberalisation by including a

linear spline function in their model, which reflected institutional changes in credit markets in

the South African economy.

Pertaining to personal saving in South Africa, they reach four main conclusions. Firstly, they

find a rise in the ratio of consumption to income in their data, and attribute this to the

financial liberalisation mentioned above, a part of which was facilitated through easier access

to housing mortgages. Secondly, they show that increasing real interest rates impact

negatively on consumption, and in fact the indirect effects of increases in the real interest rate

appear to have even larger effect on consumption than those of asset values, income and

income expectations. Thirdly, pertaining to adding income expectations as a variable in the

consumption function, they show how adding this variable actually provides a window which

allows one to see the link between personal and government saving rates – the channel

through which fiscal policy is transmitted to personal saving. Fourth, and perhaps most

importantly, they find that in the light of real interest rates and asset-to-income ratios, the

effect of a permanently higher growth rate on the personal saving ratio in South Africa would

probably be small. In estimating wealth effects on savings (and thus the personal

consumption rate) Aron and Muellbauer (2000a) use a model similar in approach to the

simple error-correction model, which weakly assumes that it is only consumption which

adjusts to restore the long-run equilibrium. This research does not make such an assumption,

and therefore proceeds with a systems approach, treating all three variables as endogenous to

the residual term; as such the model of Aron and Muellbauer (2000a) is not adopted.

Conclusion

Following the ‘outside-in’ discussion of the review of both the theoretical and empirical

literature associated with the topic, the aim of this sub-section is to state the approach to be

adopted and then, based on the literature review and the empirical findings of previous

papers, include a few outcomes one would expect to emerge in the course of the empirical

modelling.

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Selected approach

The methodology that will be undertaken in this proposed research will be based on the

theoretical framework and techniques pioneered in Lettau and Ludvigson (2004), and adapted

as per the contemporary papers listed in Table 1.

Research Hypotheses

Based on the review of the literature, an initial examination of the long- and short run

movements of consumption, wealth and income in the South African economy over the full

period in question as well as over the last decade, and given South Africa’s deeply socio-

economically inequality, the following hypotheses were put forward:

a) It was expected that a cointegrating relationship would be found linking consumption,

assets and income, at least for the period spanning 1975:Q1 to 2002:Q4; this period

ending just before the dramatic upsurge in residential property and equity values between

2003 and 2008 (Kuhn, 2010).

b) As a result of the above upsurge in household net wealth, a breakdown in the cointegrated

relationship was expected in the full sample.

c) Wealth would exhibit a significantly high transitory component.

d) Wealth would adjust significantly to deviations from the long-run trend.

e) Consumption would not adjust significantly to deviations from the long-run trend.

f) Consumption would also not respond to short-term movements in wealth.

g) Consumption would however respond to short-term innovations in income.

h) Income would adjust significantly to deviations from the long-run trend.

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Table 1: Summary of similar empirical studies for eight different economies and various ranges of data

PAPER ECONOMY and

PERIOD METHODOLOGY FINDINGS OMISSIONS

Lettau and Ludvigson (2004)

USA (1951 – 2003) DOLS, VECM, IR and VD

• Long-run relationship found • 88% of variation in asset wealth is

transitory • Consumption unaffected by transitory

changes in wealth • Trend deviation term predicts next

quarter’s asset wealth

• Did not disaggregate assets into financial and non-financial components

Chen (2006) Sweden (1980 – 2004)

VECM, IR and VD • Long-run relationship found

• Only housing wealth (residential property value) participates in the disequilibrium correction

• Almost all variance in consumption found to be permanent

• Large proportion of variance in housing wealth transitory in nature

• No omissions for a study based on macro data

Hamburg et al (2007) Germany (1980 – 2003)

DOLS, VECM, IR and VD

• Long-run relationship found

• Trend deviation predicts changes in next quarter’s income as well as other business cycle indicators e.g. the unemployment rate

• US consumption-wealth ratio (trend deviation term) predicts German stock market

• Did not disaggregate assets into financial and non-financial components

De Veirman and Dunstan (2010)

New Zealand (1990 – 2006)

DOLS, VECM, IR and VD

• Long-run relationship found • Permanent shocks account for most of

• No omissions for a study based on

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the variation in wealth • Consumption adjusts sluggishly to

restore long-run equilibrium • Consumption booms anticipate

equilibrium restoring increases in housing wealth

macro data

Corugedo et al (2006) UK (1975 – 2000) VECM, IR and VD • Long-run relationship found • Adjustment toward long-run

relationship made mainly through changes in wealth

• At least 30% of variation in asset wealth is transitory in nature

• Did not disaggregate assets into financial and non-financial components

Pichette and Tremblay (2003)

Canada (1964 – 2000)

VECM, IR and VD • Long-run relationship found • Strong residential value wealth effect

on consumption • Stock market has weak effect on

consumption

• No omissions for a study based on macro data

Fisher et al (2009) Australia (1976 – 2008)

DOLS, VECM, IR and VD

• Long-run relationship found for the bulk of the data

• Rapid rise in house prices and labour income breaks cointegrated relationship

• Residential property value transitory in nature with little effect on consumption, apart from latter data

• Non-housing consumption linked with housing wealth

• No omissions for a study based on macro data

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4. RESEARCH METHODOLOGY

This section describes the empirical methodology followed in answering the research

question. The secondary questions posed in Section 2 require quantitative answers, and thus

this section, based on the review of the empirical literature, decomposes the study into a

series of econometric procedures designed to best answer the questions posed. Following a

brief confirmation of the research approach and strategy to be followed, the literature will be

reviewed again to demonstrate in some detail the empirical approaches of the papers cited in

Table 1 above. Once these approaches have been clarified, the reader will be informed of the

particular approach followed by this paper, which has taken into account the methodologies

of these contemporary papers.

Research Approach and Strategy

By applying classical economic theory, a corresponding econometric model, and econometric

techniques to estimate solutions to the econometric model, this research paper has found an

empirical relationship between consumption and wealth in South Africa. Software was used

to implement existing theory in order to develop estimates for this relationship; therefore the

research approach was deductive in nature, and the strategy quantitative. The correct

implementation of these theoretical and practical tools however, is subject to a set of key

assumptions.

The major assumptions implicit in the approach and strategy are that (1) the life-cycle model,

based on the permanent income hypothesis, is the correct departure point for such a study (all

empirical studies reviewed in the literature have adopted this underlying theory as the basis

for their studies), (2) the model to be used is reliable and robust enough to be applied not only

to developed economies, but also an emergent economy such as South Africa, (3) the

econometric model estimation techniques are suitably robust, (4) the variables to be selected

will support the estimating power of the model, econometric tests and analysis techniques, (5)

the South African economy has been operating under steady-state conditions over the period

under investigation and finally (6) the data used to populate the variables in the model have

been recorded accurately. Given this set of assumptions, the focus now turns towards

modelling the system; it is first required to systematically develop the necessary inputs to the

system. To facilitate this, the empirical literature is now turned to.

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Review of Methodologies in the Empirical Literature

Prior to reviewing the literature, it is important to define what is meant by inputs to the

system. Treating the response to the research question as a system in itself, the inputs are

defined as the execution of the following procedures: (1) selection of variable measure in

conjunction with collection of relevant economic data, (2) transformation of the appropriate

economic data, and (3) analysis of the economic data using an econometric model, estimation

techniques and software to compute these estimates. Figure 1 illustrates this process below.

With the exception of the choice of software used, Table 2 compares these inputs against the

contemporary papers cited previously, with a detailed description of each input per paper.

Figure 15: Effect of Feedback of Data Availability on Variable Selection

Propose measures of variables to be used in

study

Check availability of corresponding economic

data

Available?

Confirm variables and transform economic

data to suit study

Conduct software-based analysis of economic

data

YES

NO

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Table 2: Comparison of Methodologies of Contemporary Papers

PAPER ECONOMY

and PERIOD

VARIABLE MEASURE USED DATA

TRANSFORMATION ECONOMETRIC TESTS PERFORMED

Lettau and Ludvigson (2004)

USA (1951 – 2003)

1. Consumption of services and non-durables net of shoes and clothing

2. Aggregated household net wealth 3. After-tax labour income

All data at quarterly frequencies, seasonally adjusted, and in real per-capita terms

1. Dickey-Fuller unit-root tests 2. Phillips-Ouliaris test for cointegration 3. Johansen cointegration for number of

cointegrating relationships 4. Stock and Watson’s DOLS 5. Johansen’s VECM 6. IR and VD according to King et. al (1991),

Gonzalo and Granger (1995) and Gonzalo and Ng (2001)

Chen (2006) Sweden (1980 – 2004)

1. Aggregated consumption 2. Housing wealth (residential property value or

non-financial wealth) 3. Financial wealth 4. Personal disposable income

All data at quarterly frequencies, seasonally adjusted, and in real per-capita terms

1. Augmented Dickey-Fuller Generalised Least-Squares test, ADF test including for outliers, Phillips Perron test, KPSS test, Zivot-Andrews test and I(1) tests to test for the presence (or non-presence) of a unit root

2. VECM analysis for long- and short-run dynamics

3. IR and VD

Hamburg et al (2007)

Germany (1980 – 2003)

1. Aggregate domestic consumption of households net of shoes, clothing, furniture and household appliances

2. Personal disposable income defined as after-tax labour income plus rental income

3. Aggregated (financial plus non-financial)

All data at quarterly frequencies, seasonally adjusted, and in real per-capita terms

1. Johansen Trace test for cointegration 2. Stock and Watson’s DOLS and Johansen

FIML for long-run estimation 3. VECM for short-run dynamics 4. IR and VD

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wealth

De Veirman and Dunstan (2010)

New Zealand (1982 – 2006)

1. Aggregated consumption 2. Housing wealth 3. Financial wealth 4. Labour income defined as after-tax wages

plus transfer income

All data at quarterly frequencies, seasonally adjusted, and in real per-capita terms

1. Augmented Dickey-Fuller unit root tests 2. Engle-Granger and Johansen tests for

cointegration 3. Stock and Watson’s DOLS for Long-run

dynamics 4. VECM for short-run dynamics 5. IR and VD

Corugedo et al (2006)

UK (1975 – 2000)

1. Consumption of non-durables and services given by aggregated consumption net of durables and semi-durables

2. Aggregated wealth given by gross housing wealth plus net financial wealth

3. After-tax labour income

All data at quarterly frequencies, seasonally adjusted, and in real per-capita terms

1. ADF and Phillips Perron for unit root tests 2. Johansen (1995) test for cointegration 3. VECM for long- and short-run dynamics 4. VD

Pichette and Tremblay (2003)

Canada (1964 – 2000)

1. Consumption of non-durables and services 2. Disaggregated wealth into (a) net domestic

and foreign assets, (b) stock market wealth and (c) housing wealth

3. Personal disposable income

All data at quarterly frequencies, seasonally adjusted, and in real per-capita terms

1. ADF and PP unit root tests 2. Johansen (1995) test for cointegration 3. VECM for long- and short-run dynamics 4. IR and VD

Fisher et al (2009)

Australia (1976 – 2008)

1. Household final consumption net of rents and other dwelling services

2. Financial wealth 3. Non-financial wealth given by the value of

dwelling assets and consumer durables 4. After-tax income

All data at quarterly frequencies, seasonally adjusted, and in real per-capita terms

1. ADF and PP unit root tests 2. Phillips Perron tests for cointegration 3. Stock and Watson’s DOLS for long-run

dynamics 4. VECM for short-run dynamics 5. IR and VD

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It is with reference to the context of the South African economy provided in Section 1,

economic theory, the review of the empirical literature as well as the context of data

availability for the South African macroeconomy that the focus now shifts towards the design

of this paper’s research methodology. Emphasis is placed on variable measure selection and

data collection, data checking and transformation, and the methods used to analyse the data

collected.

Research Design

This research paper has been designed as a longitudinal study, using time-series data to

empirically determine the relationship between three variables (consumption, income, and

wealth) for South Africa between 1975:Q1 and 2010:Q2. The process of selection of the

specific measures for these variables, and the collection of their corresponding data, is now

discussed in detail.

Variable Measure Selection and Data Collection:

Regarding variables and data, the literature review has indicated that two broad approaches

are taken by researchers when studying the consumption-wealth link. One approach is to use

macro-data, and the other is to use micro-data. The latter is often used in panel data studies to

distinguish between causal and non-causal relationships (e.g. between housing price/wealth

and consumption), as well as to identify the substitution effects of housing price/wealth on

various components of consumer expenditure (Chen, 2006). The aim of this study however

was to determine the broader relationship between consumption and wealth in South Africa,

and not the causal relationships between micro-variables, and therefore, as with the studies

listed above, macro-data has been used. The variables which describe these sets of macro data

will now be discussed individually.

Consumption

According to Lettau and Ludvigson (2004), total household consumption is given as:

�� = �a + �>a + �b + �<ca (15)

In Equation (15) ,d is total household consumption, ,e is the consumption of durables, ,fe

is the consumption of non-durables, ,g is the consumption of services and ,hie refers to the

consumption of services related to durables. Introducing further nomenclature in order to

facilitate the discussions to follow, aggregate consumption (,7) is given as ,7 = �,e +

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,fe + ,g), and the consumption of services and non-durables (,hfe) is given by ,hfe =�,h + ,fe�, i.e. the flow of consumption related to services and non-durables only.

According to Lettau and Ludvigson (2001, 2004), total consumption cannot be added to a

regression equation simply because it is unobservable, as the ,he term is not measurable.

Therefore, in all regressions involving household consumption, the value of total household

consumption must proxied; and it is in the choice of proxy (i.e. the measure of consumption

to substitute total household consumption) that the literature is undecided.

Lettau and Ludvigson (2001, 2004) argue that only the consumption of services and non-

durables should be used as a proxy for total household consumption for the following

reasons: (1) the consumption of services and non-durables is more akin to a flow of

consumption, which is more in line with the theoretical considerations of the permanent

income hypothesis; this is in contrast with the consumption of durables which pertains more

to the intermittent replacement of stock items, (2) inclusion of durables in the regression

would necessitate accounting for depreciation of the stock over time, and lastly (3) the use of

,hfe as a proxy for total household consumption is appropriate based on the assumption that

the consumption of services and non-durables is in general a constant factor of theoretical

total consumption, where:

�<>a = '�� (16)

In Equation (16) W < 1, and is the ratio of the consumption of services and non-durables to

total household consumption. This paper will however cite alternative literature and also

present a simple algebraic representation, which in conjunction with Figure 13 will provide a

theoretical justification combined with testing the assumption in (3) above against the context

of the South African macroeconomy, to proceed with ,7 as the proxy for ,d in this study.

A cursory glance at Table 2 shows that in fact, despite the above objection of Lettau and

Ludvigson (2001, 2004), four of the above authors have used some form of aggregate

consumption, ,7, as their proxies for total household consumption. Rudd and Whelan (2006)

as well have challenged the use of services and non-durables as the proxy for total household

consumption (Rudd and Whelan, 2006). Further to this, this paper now presents a self-derived

representation demonstrating why the assumption in (3) would prove weak if applied to this

study, in lieu of the history of South African consumption patterns over the last thirty five

years.

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The SARB provides four measures of household consumption in the South African National

Account: ,h, ,e , ,fe and ,he, where ,he refers to the consumption of semi-durable goods. It

is reasonable to assume that the consumption of services related to durables is a constant

fraction (call this l) of the consumption of durables. As a simplification, it also assumed that

the ratio of consumption of services related to semi-durables is a fraction not too different

from l. Thus the consumption of services related to durables may be written as:

�<ca = [��a + �<a� = [��5a�. (17)

In Equation (17) ,7e represents the consumption of semi-durables and durables, or

alternatively, ‘all durables’. Given this, total consumption may then be decomposed as

follows:

�� = '�� + �[ + ���5a (18)

Rearranging and solving for W yields:

' = � − �[ + ���5a��

Writing mnomp

as F, or the ratio of the consumption of all durables to total consumption, with

F < 1, the ratio of the consumption of services and non-durables to total household

consumption is shown to be independent of l (and thus the consumption of services related to

durables) as follows:

' = � − �[ + ��D (19)

In Equation 19, as the value of F approaches zero, W approaches 1 irrespective of the value of

l. Therefore, the value of ,hfe will then approach ,d, thereby indicating that it is incorrect to

assume that W remains a constant positive fraction. Figure 19 shows that with time, the ratio

of ,7e to ,d (less the consumption of services related to durables) has declined over the

period under evaluation, and thus, for the case of South Africa, the assumption of a constant

W is incorrect – it has been decreasing with time. The first two justifications used by Lettau

and Ludvigson (2001, 2004) above, related to the flow of consumption, are very important;

however given the lack of consensus on the topic, and a strong rejection of the assumption

underlying their third justification a system will be run using ,7, or aggregate household

consumption.

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Wealth

Granted that wealth assumes many more forms than does either consumption or income (the

various components of the South African household balance sheet have already been

discussed in Section 1), it is easy to understand the diverse disaggregation of the wealth

variable by the various studies listed in Table 1. Indeed, in the case of South Africa, with

almost 30% of total household net wealth composed of tangible assets, it would be of interest

to disaggregate the wealth variable into its financial and non-financial (tangible) components

in order to determine, amongst other parameters, the marginal propensities to consume out of

each component, as well as substitution effects between the two components. The literature

confirms that an aggregate variable may be disaggregated into economically important

components, which can lead to differing coefficients on the disaggregated wealth variables in

the regression (Fisher, Otto, and Voss, 2009).

Given access to the full data set describing the South African household balance sheet, one

may model the system depending on one’s parameters of interest, e.g. in addition to the

example above, another disaggregation could result in net wealth being split into four

components: residential property wealth, stock market wealth, remaining financial wealth and

remaining tangible asset wealth. Bearing in mind the importance of monetary policy

decisions, in all cases, it is the net value of wealth (gross assets net of debt) that is required in

the model in order not to overstate the wealth effect on consumption (Chen, 2006). It is the

use of this net value figure of the South African household balance sheet, which will now be

discussed.

Following a detailed process, Aron and Muellbauer (2006) calculated estimates of the South

African household balance sheet for the period 1975:Q1 to 2005:Q411. In the period between

2006 and 2010, the SARB has been in possession of these estimates, and has updated the

worksheet across the full period based on the methodology of Aron and Muellbauer (2006). It

is these estimates which will populate the wealth variable, for the following reasons: (1) the

methodology used by Aron and Muellbauer (2006) is similar to that used by developed

economies in estimating the personal sector balance sheet, and thus reflects not only the

standard approach to determining the net value of net market value of household wealth (and

thus the best approach currently in use internationally), but it also provides this study with a

11 This is the only reason that this study is limited to data between 1975 and 2010, since consumption and

personal disposable income figures for South African household are available from the 1960s.

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sound basis for comparison of results with those of the papers listed in Table 1, (2) the

exclusive use of JSE and housing price indices (e.g. the ABSA house price index) to capture

stock-market and residential value wealth effects respectively will not capture the full value

of wealth in the right-hand-side of the consumption function, i.e. it will ignore other

disaggregated forms of wealth which contribute significantly to aggregate net wealth, and (3),

even if all the relevant inputs were used in the right-hand-side of the consumption-wealth

relationship, Aron and Muellbauer (2006) found that not all wealth series run back to the

same date, implying that Aron and Muellbauer (2006) had to construct series using

benchmarks and international best practice, as well as convert the book values of quarterly

asset values to accumulated, market-related values. Such a task would not only be beyond the

scope of this study, it would also unnecessarily replicate Aron and Muellbauer (2006).

Therefore, in keeping with the last point above, the decision was taken to use the net value of

aggregated South African household wealth as developed by Aron and Muellbauer (2006),

and preserved by the SARB. An important point to link this sub-section with the previous one

is worth mentioning here: the value for aggregated net asset wealth12 can be used directly

when aggregate consumption is taken as the proxy for total consumption, however, the

consumption of all durables must be added to the net wealth figure when only the

consumption of services and non-durables is used as the proxy for total consumption.

Selection of the measure for the last variable in the consumption-wealth relationship, income,

will now be briefly discussed.

Income

As with the case of the measures for consumption, the measure for income (personal

disposable income) was available from Datastream and I-Net Bridge, and is the only measure

of income available from the SARB in the National Account. However, this measure of

income is the correct one for use only when using aggregate consumption as a proxy for total

consumption. The report now discusses the selection of two systems which have been

estimated for the consumption-wealth relationship for South Africa.

12 Unfortunately only the aggregated form of household net asset value could be obtained; the reasons for this

restriction will be addressed in the data collection section that follows later in this report.

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System Selection

In the initial stages of the empirical investigation, two systems were analysed (see Table 3).

The first, System 1, models aggregate consumption against aggregate net wealth and personal

disposable income. The second, System 2, models services and non-durables against the same

variables above, noting that in this system the value of ‘all durables’ (the sum of durables and

semi-durables) is now added to the value of aggregate net wealth. Note that both forms of

consumption do not equal total consumption, since total consumption is unobservable – it

includes the consumption of services related to the consumption of durables, which is not

recorded. It has already been shown that not only is the issue of modelling either form of

consumption a non-resolved issue, in the case of South Africa, the key assumption

underpinning the theoretical justification for using only services and non-durables is not

applicable. As such, this paper has run two systems in order to capture the dynamics of both

measures of consumption in relation to wealth and personal disposable income.

Table 3: Measures for Two Systems Generated

Variable System 1 measure System 2 measure

Consumption (C) Aggregate consumption (,7) Services and non-durables (,hfe)

Wealth (A) Household net wealth (qfr) Household net wealth (including

durables and semi-durables) (qfrhfe)

Income (Y) Personal disposable income (s) Personal disposable income (s)

Illustrating the above as linear relationships:

System 1 is represented as:

�5 = t�5>�, �� (20)

System 2 is represented as:

�<>a = t�5>�<>a, �� (21)

Estimating two systems has been performed in order to observe the long- and short-run

dynamics of both forms of consumption measure as opposed to just one. One may argue

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correctly that on the basis of firm theoretical considerations, only one system should be run

that captures the full effect of the consumption-wealth relationship in South Africa. However,

a further examination of Table 1 indicates how such an ‘all-encompassing’ system is non-

existent – it is seen that even studies on developed economies have tailored their systems in

accordance with data availability, theoretical considerations as well as the dynamics of those

respective economies. Despite this caveat however, the next subsection presents a summary

of justified criticisms of the two-system approach, specifically with regard to System 2.

Criticism of System 2

Chen (2006) argues that, when aggregate consumption is modelled as a proxy for total

consumption (although he uses the term ‘total consumption’, which is incorrect) personal

disposable income should be used as the proxy for human wealth, or income. The works of

Lettau and Ludvigson (2001, 2004), Pichette and Tremblay (2003) as well as Corugedo et al

(2006) corroborate this argument, as these studies use after-tax income when modelled

against the consumption of only services and non-durables as the proxy for total

consumption. One could argue in favour of System 2 by suggesting an adjustment to the

income variable whereby the corresponding values of semi-durables and durables are added

to the figure for personal disposable income (thus converting it to an ‘after-tax’ figure).

The objection to the last argument is however strongly substantiated by two points: (1) there

is no academic support for this argument in the literature, and (2) what the empirical literature

has been clear about is that when services and non-durables are modelled as a proxy for total

consumption, the value of semi-durables and durables must be added to the wealth variable.

If they were added to the personal disposable income figure as well, this double-counting

would result in an overstatement of the total wealth effect on total household consumption.

Whilst the problem above has been avoided (by only adjusting the column of wealth data, and

not that of personal disposable income), a very strong, persistent correlation emerged, during

the analysis, between �<>a and �. The existence of multicollinearity between these variables

is strongly suspected. A rigorous inspection of the SARB’s inputs to these sets of data has

also not been conducted. Based on these factors, whilst both systems have been modelled,

and the findings thereof captured and reported, only the results of System 1 will be discussed

in this report.

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Data Sampling, Checking and Transformation

This section describes the samples over which the data was collected, the means by which the

sources of data were cross-checked to ensure they corroborated each other, and lastly, it

provides a discussion of the various adjustments made to the data prior to them being ready

for inclusion in the series of tests which were conducted in the analysis portion of the

research.

Data Sampling

The data for the variables described above were obtained from the South African National

Account for the period spanning 1975:Q1 to 2010:Q2, using the I-Net portal and Datastream

(both available at the Graduate School of Business Library), and the SARB website. The

population is comprised of all inputted data as recorded by the relevant statistical authorities

in South Africa. Given this variety of sources, it was decided to cross-compare the data, to

ensure that the final data downloaded was correct.

Table 4: Sources of Data for Respective Variables

I-Net Portal Datastream SARB Website

Aggregate Consumption � �

Household Net Wealth �

Personal Disposable Income � �

Data Checking

Following a convergence, based on available data, upon the selected variables, a thorough

check of the data was performed to ensure that the correct numbers were entered into the

software estimating package. This section will briefly cover the checking procedures

performed as well as describe some of the data mining activities required to produce the

quantitative information necessary for the analysis section of the report.

All data were checked to be recorded on a quarterly frequency and seasonally adjusted. This

second point is vital; an inspection of the seasonally unadjusted data showed in general a

clear drop in consumption between the fourth quarter of a given year and the first quarter of

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the year that followed it. In order to remove this seasonal innovation, the data has been

provided in their deseasonalised form, and it is this measure that has been selected for use in

the econometric modelling to follow.

In the case of household net wealth, the SARB did not make the estimates of household net

wealth currently available. The reason for this was that the data, in possession of the SARB

since 2006, have not been published on its website. Consequently, the aggregated form of net

household assets had to be used instead. On its website, the SARB has published a series

which describes the ratio of household net wealth to personal disposable income from 1975 to

2010. This ratio has mistakenly been expressed in units of millions of rands, and ranges

between two and four hundred million. Based on Aron and Muellbauer (2006), it was

immediately identified that this ratio actually ranges between 2.0 and 4.0. It was then

determined that the numbers were comparable, and whilst the current graph on the SARB

website is based on a SARB re-calculated series from 1975 to 2010, it is held with confidence

that these ratios are correct.

Whilst the ratios are correct, the information supplied on the SARB website is that the ratios

are based on deseasonalised data, which is also incorrect. The ratio calculated by the SARB is

based on nominal, seasonally unadjusted data. However, the key information is the ratio

itself, and this ratio was multiplied by nominal, seasonally adjusted personal disposable

income, to produce a time series of nominal, seasonally adjusted household net wealth

spanning 1975:Q1 to 2010:Q2.

Data Transformation

Having produced a set of quarterly, nominal, and seasonally adjusted data for all three series,

the data were then deflated by CPI with 2005 held as the base year. This procedure is

performed so that wealth effects on consumption may estimated in the absence of the effect

of inflation; this is based on the highly justified assumption that it is not only increased

aggregate demand (driven by consumption) which causes inflation to rise. Whilst the

individual series for the components of household consumption and overall personal

disposable income are available in real terms, given that the series of household wealth

remained in nominal terms and required deflation, it was decided to deflate the nominal series

of all the data down to real terms with one deflator, i.e. the 2005 base price, in order to

achieve consistency amongst the data. Thus the data for all five variables, namely �5, �<>a,

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5>�, 5>�<>a and � are now expressed in real 2005 terms. For easier econometric

modelling, the data are expressed in their log levels.

This sub-section concludes with the issue regarding representation of the data on a per-capita

basis. This study has diverged from the general approach in the empirical literature by not

converting the data into per-capita terms. The empirical literature aims to produce a

‘representative agent’ for each economy, by dividing each series by the population of that

economy for each quarter of the data. Given South Africa’s huge economic inequality, it is

believed that such representation would be needlessly simplistic, and thus the per-capita

conversion was not carried out. Now follows a section describing the steps followed in

analysing the data.

Data Analysis Methods

This section is comprised of five sub-sections. The first four sub-sections briefly discuss the

tests performed on the data to determine their time-series properties, the long- and short run

characteristics of the system and to investigate the influence of the short-term innovations of

each variable on itself, and its sister variables. Based on a review of the considerations made

thus far, the last sub-section summarises the limitations envisaged for this study.

Unit Root Testing for Stationary Variables

Unit root testing is required to determine the time-series properties of the variables in order to

ascertain if the variables are level-stationary for difference-stationary, or I(d). The unit roots

of the level of each variable, as well as the log level of each variable were tested, using the

following three unit root testing procedures:

1. The Augmented Dickey-Fuller Test (Dickey and Fuller, 1979).

2. The Phillips-Perron test (Phillips and Perron, 1988).

3. The KPSS test (Kwiatkowski, Phillips, Schmidt, and Shin, 1992) (if the ADF and PP

results contradicted each other).

Tests for Cointegration

While some or all of the series may be individually non-stationary, there may be a

combination of these series that causes these series to ‘trend’ or move together in the long-

run. The presence of a long-run trend may be determined by testing whether the residuals of a

cointegrating equation are stationary, or I(0). This paper used the Johansen and Juselius

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(1990) method, which is considered to be the most robust test for cointegration (Johansen and

Juselius, 1990). This test for cointegration also provided the long-run elasticities of the

system.

Vector Error Correction Model (VECM) Estimation

As has been already discussed, traditional consumption studies have adopted the single

equation error correction model approach, applied in two steps. Firstly, the cointegration

equation identifies the long-run relationship between consumption, wealth and income, and in

the second step, the residual from this equation is included as an independent variable in a

dynamic, short-run equation. As mentioned before, this assumes that it is consumption alone

that adjusts to restore the long-term equilibrium of the system. It is thus more appropriate to

treat all the variables in the system as endogenous, and therefore to use the VECM (vector

error correction model) approach (Johansen, 1988) as this approach will not require one to

assume exogeneity of the independent variables, income and wealth.

However, Table 2 shows that following successful tests for cointegration, many

contemporary studies continue to use Stock and Watson’s DOLS (Stock and Watson, 1993)

technique in order to determine the long-run dynamics of the system. However, since the

Johansen and Juselius (1990) test for cointegration automatically provide one with these

long-run estimates, and the short-run dynamics can be determined from a VECM, this

research does not make use of the DOLS approach.

Impulse-Response and Variance Decomposition Analysis

Due to software limitations associated with the student version of EViews 6, it was not

possible to conduct an impulse-response and variance decomposition analysis that explicitly

separates the system into a linear combination of permanent and transitory shocks. Therefore

the following methodology has been employed to understand the responses of variables after

being influenced by the innovations in other variables (impulse response), as well understand

the proportion by which a variable is affected by its own innovations (measured using its

forecasted error) compared to that of a sister variable.

The residuals for each variable were plotted to gain an understanding of the deviation of the

actual movement of each variable from its long-run trend. Then a visual inspection of the

residuals was made so as to identify the variables whose fluctuations contained a significant

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transitory component compared to those whose fluctuations are less frequent and thus more

permanent in nature.

Thereafter, impulse-response analysis was conducted to determine the short-and long-run

implications on the level of a variable once hit by the shocks of a sister variable. Finally, a

variance decomposition analysis was performed to determine the relative contributions to

forecasted error in the future level of a variable as a result of its own innovation compared to

that of its sister variables.

Limitations

Having defined the research objectives, reviewed the relevant theoretical and empirical

literature, and formulated the research methodology, the following limitations have become

apparent:

1. An analysis of the two major components of wealth (financial and non-financial wealth)

is currently impossible due to insufficiently disaggregated wealth data.

2. The correct measure of income data (after-tax labour income), which would have allowed

for a theoretically correct analysis of services and non-durables as the proxy for total

consumption, was not available from the any of the three sources of data mentioned

above.

3. It is not possible to conduct an impulse-response and variance decomposition analysis

that explicitly separates the system into a linear combination of permanent and transitory

shocks because the software used to conduct the study (EViews 6 Student Version) does

not have this functionality.

5. RESEARCH FINDINGS, ANALYSIS AND DISCUSSION

This section is composed of three sub-sections. The first sub-section describes the detailed

procedure developed and followed to systematically analyse and record the results of the four

major procedures outlined in the previous section (i.e. unit root testing, testing for

cointegration, VECM estimation and IR and VD analysis). The second section reports the

empirical results obtained during the econometric modelling, analyses the findings and

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discusses the implications of these findings for System 1 only13. The last section deals with

limitations faced by the student during the course of the research.

Testing Procedure

Based on preliminary testing, it was noted that either a shift or a break in the cointegrated

relationship may have been present. Bearing this in mind, the following steps were carried

out, using the tests previously discussed:

1. Unit root tests in the levels and log levels of each variable, with the results tabulated and

noted (see Table 5).

2. A test for cointegration across the log levels of the full sample (1975:Q1 to 2010:Q2)

with the result noted (see Table 6). If the full sample was cointegrated with economically

intuitive coefficients14 (coefficients that are in line with the permanent-income

hypothesis) in the vector of cointegration, then it was deemed feasible to proceed with a

VECM estimation for (meaningful) discussion purposes. If it was cointegrated with

economically unintuitive results, then this result was interpreted as a misrepresentation of

the true long-run relationship within the system, due to the recent sharp rises, falls and

recoveries in residential values and equity wealth, and thus a VECM estimation was

deemed feasible only for illustrative purposes (non-discussion purposes) only. If the

sample was not cointegrated, a VECM estimation was deemed feasible but again, for

illustrative purposes only.

3. A VECM estimation across the full sample.

4. An IR and VD analysis for the full sample.

The above constituted the final results for the full-run sample. After modelling aggregate

consumption, the coefficients for the residual term were in keeping with the permanent-

income hypothesis, but since they differed so drastically from those of contemporary studies,

13 The reasons for this have been discussed in Section 4.3.1, and are restated in Section 5.2.1, prior to reporting,

analysing and discussing the findings of System 1 14 As will be shown shortly, for the case of aggregate consumption a cointegrating vector with economically

acceptable coefficients was obtained, yet further analysis demonstrated that these coefficients differed largely

from the long-run coefficients for that of a pre-2005 sub-sample.

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it was suspected that these coefficients may have differed from those of the long-run

relationship pre 2004/200515.

Thus it was of key interest to determine the long- and short-run dynamics for the system in

two ways: the first with the full-sample incorporating a dummy variable, and another option,

which preserves only the longest sample of data which produce consistent (do not fluctuate

wildly on a per-quarter basis) coefficients for the cointegrating vector. Therefore, after step

four above, the remaining steps were conducted:

5. Cointegration tests of the log levels of the data between 1975:Q1 – 1993:Q1 and the

results noted.16 It was important to preserve enough data points in the sub-sample and so

the pre-election sub-sample was chosen over a subsample which could have shed more

light on volatility in the 1980s. It was noted that factors such as the financial liberalisation

and currency volatility of the 1980s could have caused instability in the cointegrated

relationship; and therefore choosing 1986 as the breakpoint for the sub-sample sample

was considered (and in fact tested), as the implementation of the second regime of South

African monetary policy was well under way by 1985 (Aron and Muellbauer, 2000b).

However, during testing over this period (e.g. 1975:Q1 – 1983:Q1, 1975:Q1 – 1984:Q1,

etc.), large instability was noted. It was unclear if a small sample size contributed to this

more than the volatility within the data. Therefore a decision was made to formally

proceed with analysing the pre-election 1975:Q1 – 1993:Q1 sub-samples only.

The pre-election (or apartheid) sub-sample however does capture the information

contained in the proposed 1975:Q1 – 1986:Q1 sub-sample, as well as an additional seven-

year period of volatility; being the politically turbulent build-up to the first democratic

election in South Africa’s history, and a period of massive government dis-saving in the

run-up to 1994 (Aron and Muellbauer, 2000a). However it will not capture a possible step

response created by the instatement of the then newly-elected ANC government.

15 Additionally, modelling services and nondurables provided long-run parameters that violated the permanent-

income hypothesis (they suggested a negative correlation between asset wealth and consumption). 16

Due to length limitations the results of the cointegration tests in this step are not presented in this report but are available on request from the student.

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As such, yearly increments were used after the pre-election sub-sample, starting from

1975:Q1 – 1994:Q1 until 1996, looking for the step change in the consumption-wealth

relationship. However, a step change, break or even significant shift in the co-trended

relationship was not found over this period. In order to investigate the effects of the

wealth bubble discussed in Section 1, the attention of the analysis then shifted towards the

2000-2005 period.

Bearing in mind that the consumption of services and non-durables seemed, from the

discussion in Section 1, to respond faster than that of durables to permanent changes in

total wealth, a sub-sample between 1975:Q1 to 2002:Q1 was tested for System 1 (and a

sub-sample between 1975:Q1 to 2000:Q1 tested for System 2, the results of which are

available on request), with yearly increments taken thereafter. For an optimal lag length

(the criteria for which will be discussed shortly), a point was identified where the first

major shift in the cointegrated relationship occurred17. Following this, two approaches

were then employed; the insertion of a step dummy variable at this point (Step 6) and

splitting the sample (Step 9) just before the point of the major shift:

6. Introduction of a dummy variable into the cointegrating space at a selected point where it

was estimated that the shift in the co-trended relationship occurred, and based on tests for

cointegration incorporating the dummy variable, the ‘best’ year and quarter (e.g.

2004:Q4) selected, with the dummy variable positioned there, set to run as ‘1’ until the

end of the full sample.

7. VECM analysis for the cointegrated relationship estimated in Step 6.

8. IR and VD analysis for the VECM analysis in Step 7.

9. Splitting of the sample just before the point of the major shift in the co-trending

relationship, and a test for cointegration. The aim here was to preserve as many data

points which most accurately describe the wealth-consumption relationship in South

Africa (i.e. without large disturbances, like that of the large wealth bubble of 2003 –

2007).18

17 This reference to System 2 is made purely to corroborate the earlier thoughts in this paper regarding the

relative response rates of the respective measures for consumption in responses to wealth effects – it was found

that the shift-point occurred approximately one quarter earlier for CSND than CA. 18 Once again these results are not presented in this report due to space constraints but are available from the

student on request.

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10. Tabulation and discussion of selected results for cointegration, VECM and IR and VD

analyses. These will include the results for the full-run sample alone, the full-run sample

with a dummy variable, and the sub-sample of step 9.

As has been previously discussed, the basis of the empirical approach selected relies upon the

condition that the three variables are cointegrated, i.e. they form a linear combination, the

residual of which does not contain a unit root. If this is the case, use of a vector-error

correction model to determine the short-run dynamics of the system is then feasible.

However, as is standard practice, each variable is subjected to a series of tests to determine its

own time-series properties, specifically to determine whether it itself contains a unit root in

its own level, or log level.

Empirical Findings, Analysis and Discussion

As discussed in the last paragraphs of Section 4.3.1, the empirical literature unanimously

agrees that when aggregate consumption is used as the proxy for total consumption, personal

disposable income should be used as the proxy for human wealth, or income. If the

consumption of only services and non-durables is used as the proxy for total consumption,

then after-tax income must be used as the corresponding measure for human wealth. The only

measure for human wealth available to the student was personal disposable income. It is

suspected that it was this mismatch of variables that resulted in a very strong, persistent

correlation between �<>a and � during testing, thereby suggesting the presence of

multicollinearity between these variables. Therefore only the results of System 1 will be

discussed in this report.

Unit Root Testing

The levels and log levels of all five variables were tested for I(0) non-stationarity using the

Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests. Each test is based on the null

hypothesis that the variable under scrutiny is I(0) non-stationary i.e. it contains a unit root in

its level and log level. For both the level and log level of each variable, two separate

assumptions were incorporated for both the ADF and PP tests, namely that the variable

contained an intercept (constant) or a deterministic (linear trend) term in its overall trend.

With the exception of one case, the ADF and PP tests corroborated each other strongly (see

Table 5 for a summary of the unit root tests). This exceptional case is discussed next.

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The last pair of ADF and PP tests, which investigated the non-stationarity of the log level of

income, assuming a trend and intercept in the data, produced contradictory results, with the

null hypothesis not being rejected in the ADF test, and being rejected in the PP test. In this

case, the KPSS test was used to decide the matter; the result of this test was that its null

hypothesis was rejected, i.e. the null hypothesis of stationarity was rejected since the test

statistic was higher than that of the 1% level; a strong rejection. Thus, all the variables, in

both their levels and log levels, contain unit roots, i.e. they are I(1) stationary.

Table 5: Unit Root Test Results

The next section presents the results for cointegration and VECM analysis for the system.

The analytical procedures, problems faced and assumptions made by the student in

developing these estimates will be dealt with in a detailed manner, along with an analysis and

discussion of the associated quantitative findings.

Cointegration Testing and VECM Estimation

Tests for Cointegration

Using the methodology of Johansen (Johansen, 1995), EViews 6 Student Version allows the

user to compute tests for cointegration. The precondition for conducting a test for

cointegration is that all the variables must contain unit roots in their levels or log level; for

this study this precondition was already met, being confirmed through the unit-root testing

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procedure previously discussed. The next step was to select a critical significance level and

lag length. Based on the results of an unrestricted VAR, the optimal lag length of 1 was

selected based on the Schwartz Information Criteria (SIC)

Having determined the optimal lag, the test for cointegration within the system was then run,

subject to the user-specified critical value taken from MacKinnon-Haug-Michelis

(MacKinnon, Haug, and Michelis, 1999). Table 6 summarises the results of the trace and

maximum eigenvalue tests19. One significant cointegrating equation was found at the 1%

level of significance.

Table 6: Johansen Cointegration Results

VECM Estimations

Long-run dynamics

Following the methodology of Lettau and Ludvigson (2001), the long-run relationship

between consumption, aggregate wealth and income may be written in terms of the trend

residual, or ��u�, where:

2�\N = 2� − ?��vM − ?NN − ' (22)

In Equation, the lowercase letters indicate that the variables are in log levels. Hw and Hx are

the long-run elasticities (Cutler, 2005), or steady-state shares of assets and income in total

wealth respectively, given by:

?� = 5>�� (23)

19 According to the methodology of Lettau and Ludvigson (2004), deterministic trends should not be included in

the cointegrating space and thus the results of System 1 were accepted but the results of System 2 were rejected.

Hypothesized Trace 5% Hypothesized Max-Eigen 5%No. of CE(s) Eigenvalue Statistic Critical Value No. of CE(s) Eigenvalue StatisticCritical Value

None *** 0.208 47.177 29.797 None *** 0.208 32.717 21.132At most 1 0.097 14.460 15.495 At most 1 ** 0.097 14.334 14.265At most 2 0.001 0.126 3.841 At most 2 0.001 0.126 3.841

Trace Test Max Eigenvalue Test

Lags interval (in first differences): 1 to 1 based on the Schwartz Information Criteria (SIC). Trace test and max-eigenvalue test indicates 1 significant cointegrating equation at 1% significance level. The 5% critical values are based on Johansen and Juselius (1990).

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and,

?N = �� (24)

?� + ?N = � (25)

Ignoring the constant above, the long-run dynamics between consumption, wealth and

income are therefore given by (Note Table 7 below):

2� = �. ��y�vM + �. z{N (Full-run sample) (26)

2� = �. ||�vM + �. y| − �. �}~@��N (Dummy sample) (27)

2� = �. |��vM + �. y|N (Sub-sample) (28)

Movements in long-run coefficients

Comparing the coefficients for the sub-sample and the full-run sample, the coefficient on

aggregate wealth has reduced to almost a quarter of its original value, whilst the coefficient

on income has increased by just over 40% of its original value. This may constitute a

substitution effect, where a large portion of consumption has now shifted from spending out

of wealth to spending out of income. However there is an alternative argument to this.

Aggregate wealth, over the period where the break in the original cointegration equation

occurred, increased by a huge amount. Therefore, if consumption increased, but not by the

same scale as that of wealth, then it makes sense that even if there was no substitution effect,

the coefficient on wealth would be smaller simply because the aggregate wealth in the system

was so much greater than its pre-bubble value.

However, income also increased considerably towards the end of the decade. This probably

suggests that, as a result of a permanent increase in total wealth, the permanent increase in

consumption was made more out of personal disposable income as opposed to asset wealth.

Considering South Africa’s deeply economically unequal society, and that a minority of the

population is in possession of most of the aggregate wealth in the system, this seems to be a

plausible conclusion, and it also serves to resolve the question as to why the coefficient on

wealth decreased, yet the coefficient on income increased. Therefore it could be argued that

the permanent component of the increase in total wealth in the system led to a permanent

increase in consumption which was borne out of a disproportionate increase in the

consumption out of income. It is important to bear in mind that the t-stat of Hw in the full

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sample, while significant at the 5% level, is much weaker than that of the sub-sample, which

is strongly significant. This perhaps justifies using the results of the sub-sample as a more

accurate reflection of long-run consumer behaviour in South Africa. The discussion now

turns toward an examination of the wealth bubble.

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Table 7: Cointegration and VECM Results (for System 1) for a Full-Range Sample, Full-Range Sample including a Dummy Variable at 2005:Q2 and a Long-Range Sub-Sample

AGGREGATE CONSUMPTION

Full-run sample Dummy sample Long-run Sub-sample 1975:Q1 - 2010:Q2 1975:Q1 - 2010:Q2 (dummy @ 2005:Q2) 1975:Q1 - 2005:Q1

Long-run from FIML

Normalised cointegrating coefficients

1/c βa βy 1/c βa βy βdummy 1/c βa βy

1 0.104764 0.758986 1 0.435583 0.541535 -0.125739 1 0.429601 0.535413

t-stat [-2.33142] [-17.6754] [-7.37832] [-11.8929] [ 5.48146] [-6.13485] [-10.1373]

Short-run from

VECM

Adjustment (t) ∆c(t) ∆a(t) ∆y(t) ∆c(t) ∆a(t) ∆y(t) ∆c(t) ∆a(t) ∆y(t) Residual (t-1) -0.120266 -0.182754 0.420145 -0.146552 0.199724 0.214566 -0.161702 0.205689 0.271619

t-stat [-3.11242] [-1.23624] [ 4.09732] [-4.63676] [ 1.60712] [ 2.36449] [-4.38159] [ 1.46255] [ 2.47265]

∆c(t-1) 0.181378 -0.19316 0.488296 0.093356 -0.169689 0.67135 0.049569 -0.304486 0.635675

t-stat [ 2.16989] [-0.60402] [ 2.20130] [ 1.15104] [-0.53211] [ 2.88303] [ 0.56633] [-0.91286] [ 2.43991]

∆a(t-1) 0.028755 0.134418 0.139486 0.001531 0.225582 0.136651 -0.014108 0.188544 0.142849

t-stat [ 1.23102] [ 1.50413] [ 2.25021] [ 0.06404] [ 2.40052] [ 1.99145] [-0.51952] [ 1.82199] [ 1.76730]

∆y(t-1) -0.049975 0.08681 -0.125055 -0.044712 0.21852 -0.229397 -0.05209 0.222475 -0.220996

t-stat [-1.51522] [ 0.68798] [-1.42878] [-1.51055] [ 1.87760] [-2.69933] [-1.67882] [ 1.88154] [-2.39287]

Dummy n/a n/a n/a n/a n/a n/a n/a n/a n/a

t-stat n/a n/a n/a n/a n/a n/a n/a n/a n/a

Constant 0.00624 0.007391 0.004962 0.006989 0.004873 0.004529 0.007449 0.005842 0.005234

t-stat [ 5.26639] [ 1.63059] [ 1.57804] [ 6.00105] [ 1.06416] [ 1.35469] [ 5.78916] [ 1.19145] [ 1.36670]

R-squared 0.129079 0.048768 0.22037 0.197154 0.073785 0.158748 0.170207 0.05104 0.161685

� Numbers in bold black indicate significance at the 5% level � Numbers in bold blue indicate significance at the 10% level

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Examination of the Wealth Bubble

As can be seen, insertion of the dummy variable in System 1 has restored the beta

coefficients to approximately the same values they were prior to the tremendous increase in

total wealth in the system. The role of the bubble dummy is to represent the long-run

relationship in terms of what it was before the wealth boom (i.e. preserve the old

coefficients), yet quantitatively describe the difference between the new total wealth in the

system and the actual amount of wealth taken up as consumption by households. Whilst the

coefficients remain the same, the values of aggregate asset wealth and income increased

significantly, and the value of the bubble dummy is quantitatively large when expressed in

rand terms. One of the main findings of this paper is the identification and confirmation of a

significant disturbance to the long-run relationship between consumption and wealth in South

Africa, that is, the large wealth bubble which occurred in the latter half of the last decade. A

few theoretical findings are discussed next.

Evaluating the Sub-Sample Beta Coefficients

From Equation 25 the elasticities of aggregate asset wealth and income must sum to unity. In

the case of the sub-sample, the sum of the coefficients is 0.97, extremely close to this

theoretical figure. However, one would expect that if total consumption is not observed (and

therefore recorded) that when the left hand side of Equation 28 is normalised to unity, the

sum of the coefficients of the right-hand side variables would exceed unity, since they will be

divided by a fraction equal to the ratio of observable (in this case aggregate) consumption to

total (theoretical, unobservable) consumption. An examination of the empirical literature

shows that often, the sum of the right-hand side coefficients do not always tally with text-

book theory. Given the above however, the value of 0.97 is extremely close to the theoretical

value of 1; this results in asset wealth’s relative contribution to total wealth equalling 0.43,

with that of personal disposable income equalling 0.54. Based on these elasticities, the

marginal propensities to consume out of aggregate wealth and personal disposable income are

now computed.

Computing the MPCs

According to Cutler (2005), the marginal propensity to consume out of wealth is given as �m�r.

Given that the elasticity is defined as �m/m�r/r, then computation of the MPC is achieved by

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simply dividing the elasticity of wealth by the average ratio of wealth to consumption across

the full set of data. This ratio has been computed from the data sets; it equals 3.03. Therefore

the marginal propensity to consume out of net asset wealth in South Africa equals 0.1485. In

other words, given a permanent increase in wealth of R1, consumption should be expected to

increase permanently by 15 cents. This number is approximately three times given by the

empirically-derived “rule of thumb” of 5 cents20 (Ludvigson and Steindel, 1999). The

corresponding MPC out of personal disposable income is 0.598, which means that almost 60

cents out of every rand of a permanent increase in personal disposable income is consumed in

the long run. While these numbers seem unrealistic, it must be remembered that the long-run

elasticities generated were not too dissimilar from those the several empirical papers

researched. Indeed, there is a wide range of beta coefficients across these economies.

Therefore, the problem must lie in the ratios against which the corresponding elasticities were

post multiplied. It is based on this consideration that the discussion now turns towards

providing an explanation for these MPCs.

Explaining the MPCs

Table 8: Cross-comparison of varying Elasticities and MPCs by Economies studied in the Literature

Germany

(Hamburg et

al, 2006)

New Zealand

(De Veirman

and Dunstan,

2010)

England

(Corugedo et

al, 2006)

Australia

(Fisher et al,

2009)

USA (Lettau

and

Ludvigson,

2004)

Elasticity of

wealth 0.31 0.28 0.25 0.25 0.33

Elasticity of

income 0.74 0.68 0.60 0.8161 0.67

MPC out of

wealth 0.044 0.147 0.058 Not available 0.055

MPC out of

income Not available Not available 0.05 Not available Not available

20 This is based on developed economies; a discussion of this important point follows later.

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Upon inspecting Table 8 it is evident that the long-run elasticity of income for South Africa is

very close to that for England, and not too dissimilar from those for New Zealand and the

USA. However, the MPC out of income for England is only 0.050, compared with South

Africa’s 0.598. This obviously implies that the average ratio between income and

consumption in England is far higher than that of South Africa’s. Despite New Zealand’s

elasticity of wealth being almost twice that of South Africa’s, due to a wealth to consumption

ratio of 2, its MPC out of wealth is very close to that of South Africa’s, almost identical.

What this discussion seems to imply is that the MPC is not just an indication of long-run

consumer behaviour in an economy. It also is an indicator of the legacy of long-run

consumption spending vs. saving habits, as well the earning power of the household sector in

an economy. A country with high elasticities of wealth and income respectively, may have

relatively low marginal propensities to consume out of wealth and income simply because its

ratio of wealth to consumption and ratio of income to consumption are relatively high.

Nevertheless, South Africa’s high MPC out of household net wealth is indicative of a poor

history of personal saving, thus confirming the literature presenting this opinion in Section 1.

In relation to its saved personal wealth, South Africa’s long-term household consumption rate

is very high, and should remain a key concern to policy makers. Additionally, the MPC out of

personal income is staggeringly large suggesting that long-term plans should be introduced to

promote household savings. These issues are dealt with again in Section 6. The short-run

dynamics of the system are now discussed.

Short-Run Dynamics

This section will first discuss the similarities across the samples for System 1, and then pays

attention to specific dynamics within the sub-sample. Only those coefficients which were

significant at least the 10% level will be mentioned in the first part of the discussion. When

discussing the dynamics pertaining to the sub-sample, the 5% level of significance will be

used to filter out relatively unimportant dynamics within the sub-sample, and a more

extensive analysis and discussion of these dynamics will be provided.

Similarities across Samples

Across all three samples it is quickly observed from Table 7 that consumption and income

adjust in the next quarter to restore the disequilibrium in the current quarter. Another strong

coefficient which emerges is the power of today’s change in consumption to predict next

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quarter’s income growth. In all the samples, at the 10% level of significance, asset growth in

the current quarter predicts next quarter’s change in income.

Short-Run Dynamics in the Sub-Sample

The estimated coefficient on the error-correction term is sizeable and statistically significant

at the 5% level in both the income and consumption equations, indicating that when private

saving is low (the error correction term is then positive), it is consumption that falls in the

next period, whilst income rises in the next period to restore the long-run relationship whilst

aggregate wealth does not adjust significantly; when private saving is high (the error

correction term is then negative), it is consumption that rises in the next period, whilst

income falls. Of great interest is the next observation, that of consumption growth today

strongly predicting next quarter’s growth in personal disposable income.

By consumption predicting income, it is meant that consumers actually increase their

spending (and thus decrease their savings) when their expectations are that income in the next

quarter is set to rise. This is perfectly in line with the life-cycle model (Ando and Modigliani,

1963), which is based on the assumption that the average consumer will attempt to smooth

his or her consumption in relation to expected income. In light of warranted expectations of

an increase in next quarter’s income, South Africans in general spend more in today’s

quarter. This results in an increase in a deviation from the long-run relationship between

aggregate wealth, income and consumption, which is corrected by an increase in income in

the next quarter, occurring contemporaneously with a decrease in consumption. Asset wealth

does not contribute to the long-term correction, and short-run movements in asset wealth are

not associated with short-run movements in consumption.

Correspondingly, what this does imply is that short-term consumption and personal

disposable income are very closely tied together in South Africa. Considering that

consumption is intuitively more evenly spread across the population than are financial wealth

(a large portion of which is composed of equity wealth) or residential/tangible asset wealth, it

is not surprising that short-term consumption is not linked significantly with asset wealth –

consumption in the short term is taken out of income, and not assets. Income it appears

contains a strong transitory component which is mean-reverting, adjusting over the short-term

to restore the long-run equilibrium. Consumption, it is seen, also adjusts in the next quarter,

but is also driven by short-term expectations of future income. Based on the review of the

empirical literature, these short-term dynamics are unique to the South African economy;

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only the study for Australian data spanning 1976 – 2008 are similar: in that study it was

found that consumption also decreased in the next quarter to restore the equilibrium, but with

non-financial assets expected to rise contemporaneously, and not income (Fisher, Otto, and

Voss, 2009).

The results above accord with the conclusions reached at the end of the section dealing with

the long-run dynamics of the system. One of the outcomes in that section was a concern over

the large MPC out of income, over the long-term. Given that income and consumption are so

closely linked in the short-run, the value of the MPC is not surprising; the long- and short-run

estimations of the system corroborate each other. Given its low wealth-consumption ratios, a

large disparity in asset ownership across the population and low levels of personal disposable

income in the aggregate, the high long-run level of consumption out of personal disposable

income by the South African household sector is unsurprising, and is a major concern, with

both short- and long-term implications on inflation and investment-driven medium-term

growth in the economy. Hence the impulse-responses (IR) and variance decompositions (VD)

of the System 1 sub-sample will be discussed further below.

IR and VD Analysis

The objective of undertaking the IR and VD analysis is so as to answer the last two remaining

research questions. Since it was not possible to use the technique of Gonzalo and Ng (2001)

to explicitly decompose the permanent and transitory elements (Gonzalo and Ng, 2001), a

three-stage process was adopted. Firstly, the plotted residuals were inspected to rank the

variables in order of the degree of the transitory component within each variable.

Then, the outputs of the impulse response functions were generated for the system to

determine the levels at which variables within the system are impacted by innovations within

the system. Lastly, variance decomposition analysis was undertaken to ascertaining how

much of the variance in each variable is explained by its own shocks in relation to the amount

of variance in the variable explained by innovations of the other two variables in the system.

Inspection of the Residuals

Referring to Figure 16 below, it is clear that the range of the deviation of aggregate

consumption from its long-run trend is much lower than that of aggregate wealth and income,

with the latter two deviating from their respective long-run trends over a similar range for the

period 1975:Q1 to 2005:Q1. Aggregate wealth has a very persistent and large transitory

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component it seems, as is the case with income, but it must be borne in mind that this sample

excludes the wealth bubble which commenced around 2003-2005.

Figure 16: Residuals of the System 1 Variables across the Sub-Sample Period

By inspection it appears that aggregate wealth contains the largest transitory component,

followed by personal disposable income.

IR and VD Analysis

The results of an impulse response and variance decomposition analysis are highly sensitive

to the ordering of the variables. Based on limited information regarding the transitory

components of the variables, it was difficult to justify any particular ordering and as a result,

when generating the impulse response curves and table provided below, the option used was

‘Generalised Impulses’ (Pesaran and Shin, 1998), which does not depend on the ordering of

the variables The results for all six possible responses were then generated and compared

graphically with those produced by the impulse response analysis. Thereafter the student

specified the ordering on the basis of similarity with the original graphs from the IR output.

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Using this process suggests the following order of (1) consumption, (2) wealth and (3)

income, which is also supported by Lettau and Ludvigson (2004) who use the same ordering

when conducting their analysis of American consumption, wealth and income.

Figure 17: Impulse Response Analysis of System 1

The above curve shows how, in line with the VECM analysis, aggregate consumption starts

off in quarter 1 at a ‘high’ value in expectation of an increase in income in the next period.

The value of consumption then decreases in the following quarter to restore the equilibrium,

along with the associated growth in income. It is also apparent that within just over 6

quarters, consumption is restored to its previous value, suggesting that presumed transitory

fluctuations in both income and wealth are not associated with a permanent increase in

consumption.

The variance decomposition of aggregate consumption shows that for the first two quarters

following shocks to the systems from all the variables, more than 97% of the forecasted error

for aggregate consumption is explained by itself. This conclusion is very similar to that of

Lettau and Ludvigson (200421.

21 For the sake of brevity, all six combinations (CAY, YAC, ACY, AYC, CYA and YCA) of variable ordering

were tested but not included in this report.

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Table 9: Variance Decomposition of the Sub-Sample Period for System 1

Variance Decomposition of LOGTC:

Period S.E. LOGTC LOGW LOGY

1 0.011844 100 0 0

2 0.016591 97.58624 1.917804 0.495952

3 0.020971 89.48964 6.997307 3.513049

4 0.02553 80.66009 12.8923 6.447608

5 0.029983 73.61503 17.67149 8.713483

6 0.034183 68.52434 21.17613 10.29953

7 0.03808 64.89944 23.6934 11.40716

8 0.041688 62.27883 25.52333 12.19784

9 0.045041 60.33516 26.88499 12.77985

10 0.048174 58.85315 27.92517 13.22168 Variance Decomposition of LOGW:

Period S.E. LOGTC LOGW LOGY

1 0.045134 4.182064 95.81794 0

2 0.066834 4.131545 95.54414 0.324318

3 0.081505 4.811748 94.95347 0.234781

4 0.09184 5.266118 94.34302 0.390862

5 0.099956 5.620868 93.64544 0.733692

6 0.106841 5.895719 92.95885 1.145436

7 0.113004 6.11512 92.3298 1.555079

8 0.118701 6.2941 91.77594 1.929964

9 0.124069 6.44294 91.29633 2.260726

10 0.129183 6.568687 90.88271 2.548602 Variance Decomposition of LOGY:

Period S.E. LOGTC LOGW LOGY

1 0.035253 6.162315 1.486742 92.35094

2 0.044489 17.67734 1.057695 81.26497

3 0.051933 20.34381 1.670331 77.98586

4 0.05813 22.38167 2.409193 75.20914

5 0.063629 23.66005 3.181125 73.15882

6 0.068643 24.57759 3.866702 71.55571

7 0.073295 25.26111 4.446243 70.29265

8 0.07766 25.79203 4.926405 69.28157

9 0.081789 26.21675 5.323566 68.45968

10 0.085717 26.56465 5.654233 67.78112 Cholesky Ordering: LOGTC LOGW LOGY

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6. CONCLUSION

This conclusion is comprised of three sub-sections. Based on the empirical findings produced

in this paper, the first sub-section addresses the primary research question by providing

explicit answers to the sub-questions listed in Section 2. The second sub-section lists and

discusses the additional findings made by this paper. Providing a comprehensive discussion

of the key themes running through the paper, the third and last sub-section also describes the

implications of the study, and how these implications are relevant to South African monetary

policy.

Answers to the Research Questions Posed

Answers Relating to the Long-Run Dynamics

1. Do the variables consumption (C), assets (A) and income (Y) have one or more

cointegrated relationships?

The variables consumption, asset wealth and income were co-trended across all the samples

for System 1, with the presence of one cointegrating vector significant at the 1% level.

2. What are the respective shares of income and assets in total wealth in South Africa?

The relative shares of asset wealth and human wealth in total wealth are 0.43 and 0.54

respectively. These figures are based on the beta coefficients in the cointegrating vector for

the sub-sample of System 1, which models aggregate consumption as its proxy for total

consumption. The sub-sample was selected as it is the truer representation of long-run

consumer behaviour in South Africa, since it does not include the effects of the wealth bubble

present in the last five years of the data.

3. How can the long-run response of household consumption in South Africa be

described (what are the marginal propensities to consume out of assets and income

respectively and how do these MPCs compare with those of developed economies such

as the USA, Canada, England, Germany, Sweden, Australia and New Zealand)?

The South African marginal propensities to consume out of aggregate wealth and income are

0.1485 and 0.598 respectively. Whilst the MPC out of income is not usually of much interest

in the literature (as compared to the MPC out of wealth), the MPC figure computed for

income is extremely high when compared to that of a developed economy such as England.

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The MPC out of wealth is also very large and approximately three times the typical value

associated with Anglo-Saxon economies. Given (1) a vast socio-economic disparity within

South Africa, (2) the differences in structure between its economy and those of European or

North American economies (as indicated by the elasticities computed) and (3) the far smaller

ratios of wealth and income to consumption in South Africa as compared to its developed

counterparts, the relevance of such comparisons may be questioned. However, granted that

South Africa is an emerging market seeking to develop into a first-world economy, the topic

of long-run consumer behaviour in relation to accumulated total household wealth cannot be

discussed without some comparison made to first-world economies. Given this, the large

marginal propensities to consume out of income and wealth should be of major concern to

macroeconomic policy makers in the long run; this concern will be discussed in more detail

later in this conclusion.

4. Have there been wealth bubbles that have structurally broken the long-run relationship

between household consumption and wealth; and if so, is there evidence of a

breakdown in the cointegrated relationship across the full sample of data to support

this?

A wealth bubble was found in the full-run sample of data, by detecting a major shift in the

cointegrating relationship over 2005:Q2 for System 1. Technically the cointegrating

relationship did not break; however in quantitative terms the long-run parameters of the

cointegration equation shifted significantly. The quantitative significance of the wealth

bubble is represented by the value of the dummy variable; when expressed in rand terms this

value equates to approximately R144 billion of wealth in the system per quarter which does

not contribute to household consumption.

Answers Relating to the Short-Run Dynamics

1. How do the short-run movements in the long-run relationship influence each of

consumption, assets, and income and which variable contributes most to the long-term

correction?

Regarding the short-term deviations of the cointegrated relationship, it has been demonstrated

that only income and consumption adjust to restore the long-run equilibrium. In order to

compensate for a positive error-correction term in the current quarter, consumption decreases

in the next quarter with income increasing. Asset wealth does not participate in the error

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correction. These results indicate a strong short-term relationship between the co-movements

of consumption and income.

2. How does each variable respond to temporary changes in the variables in the previous

quarter (including its own change)?

Consumption growth in today’s quarter is a strong predictor of income growth in the next

quarter. What this suggests is that South African short-term consumption is strong linked to

warranted expectations of increased future income. If South Africans know with certainty that

future income will rise next quarter, then household consumption will increase in the current

quarter. This finding is in line with conventional economic theory. It also underlines the

strong relationship between the short-run movements of consumption and income

respectively, and provides a key insight into explaining the long-run marginal propensity to

consume out of income. Statistically significant, today’s growth in income also predicts

tomorrows decrease in income, suggesting that income does not follow a random-walk, but

that its future value is predictable once a measure of its growth in the current quarter is

known. Very importantly, whilst the results indicate a strong relationship between the short-

term movements in consumption and income, the transitory, short-term movements of asset

wealth are not associated with short-term fluctuations in consumption.

3. How do these short-run dynamics compare with those of developed economies (such as

the USA, Canada, England, Germany, Sweden, Australia and New Zealand)?

Based on a comparison with other studies, the short-run results produced for South Africa are

unique. The trend residual predicts asset returns for both the USA (Lettau and Ludvigson,

2001; Lettau and Ludvigson, 2004) and England (Fernandez-Corugedo, Price, and Blake,

2007), whereas in the case of Germany (Hamburg, Hoffmann, and Keller, 2008) it predicts

only income. Short-run adjustment to restore equilibrium occurs through movements in

consumption and non-financial wealth for the Australian (Fisher, Otto, and Voss, 2009) and

New Zealand (De Veirman and Dunstan, 2010) economies, and through stock-market and

housing wealth for Canada (Pichette and Tremblay, 2003). As has been mentioned before,

adjustment for deviations in the long-run trend in the South African economy occurs through

short-run movements in consumption and income, with current consumption growth also a

strong predictor of future income gains.

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4. What proportion of the variance in each variable is attributable to the influence of each

of the other variables?

Based on the results of the variance decomposition it is observed that over the course of two

quarters, almost 98% of the variance in consumption is explained by shocks caused as a result

of its own transitory movements. This implies that while consumption responds to the error-

correction term, it is not affected by temporary fluctuations in asset wealth or income. It

appears that temporary changes in consumption are driven more by warranted expectations of

increases in future income.

5. What is the duration of the shock, and thus influence, of one variable on another?

The results of the impulse response analysis indicate that asset wealth and income are

significantly more affected by transitory shocks than is consumption, which experiences a

relatively small change in its level that, in the absence of further disturbances on the system,

corrects within six quarters.

Additional Findings

The Effect of the 1994 Elections on the Consumption-Wealth Relationship

There was no significant shift in the cointegrated relationship over period which spanned the

1994 election.

The Effect of Volatility in the Data during the 1980s

During investigation of the system, experimentation with different sample periods was

undertaken (e.g. 1980 – 2010, 1985 – 2005, etc). The results of these experiments revealed a

significant breakdown in the cointegrated relationship during the 1980’s, suggesting a large

increase in household dis-saving during that period, following easier access to consumer

credit. The period under examination coincided with the start of the second monetary regime,

which was fully in operation by 1985 (Aron and Muellbauer, 2000b).

Key Themes and their Implications on South African Monetary Policy

Significance of the Concept of an MPC for South Africa

As was explained in Section 5.2.2, the large marginal propensities to consume out of wealth

and income for the South African economy are a function of not only long-run consumer

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behaviour in South Africa but also a function accumulated wealth and the current level of

aggregate income in the economy. Therefore the MPC estimates provide information not only

about the current state of the macroeconomy but also about its historic saving rate.

The MPC has value perhaps only as a relative measure, to be used in comparison with

estimates based on the long-run characteristics of other economies. Although South Africa is

an emerging country, it is insightful to compare the computed MPCs for the South African

economy with those of first-world economies. Following on from this, based on the findings

reached by this report, as well as through the argumentation of Aron and Muellbauer (2000a),

monetary policy in South Africa must look to promote the personal sector saving rate. An

increased rate in household saving will result, in the long-run, in increased aggregate asset

wealth and income levels, thus reducing the MPC estimates and bringing the South African

macroeconomy more into line with the long-run consumption behaviour of first-world

economies. However, two questions now emerge: (1) do the short-run dynamics of

consumption affect the long-run relationship, and if they do, given the high level of socio-

economic inequality in South Africa between the rich and poor, whose responsibility is it to

save in the short-run? A discussion around these two questions is presented next.

Short-Run Consumer Behaviour, Income and Aggregate Wealth in South Africa

It has been demonstrated that in the short-run, household consumption in South Africa is

disassociated with fluctuations in asset wealth, whilst the co-movements of income and

household consumption are closely related. Based on the empirical analysis, it has been

concluded that household consumption increases in light of information of expected increases

in future income. The results make intuitive sense. Based on the discussion in Section 1

pertaining to the South African household balance sheet, only 8.8% of asset wealth is in

monetary assets, with 30% comprised of tangible assets and the remaining 60% in pension

funds and equities (Kuhn, 2010).

Under the assumption that the bulk of the South African population is not invested in stock-

market wealth, nor has access to credit via the collateral channel, short-term fluctuations in

equity prices or residential property values would not be transmitted onto the majority of the

household sector. This along with a relatively low aggregate level of income, unsurprisingly

results in a strong short-run dependency on expected levels of future income, with corrections

to the system made only by changes in next quarter’s income and consumption levels. The

long-run relationship therefore reflects a strong marginal propensity to consume out of

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income. Based on these considerations, South African monetary policy should look to

promote short-term saving, or decreased household consumption, out of income, of that

segment in possession of the bulk of the net asset wealth in the household sector. With

increased savings from this segment of the household sector, aggregate wealth and income

will in the long-run increase, thus promoting medium- to long-term growth, as well as

dampening long-term inflation.

The short-run dynamics of the cointegrated relationship work to preserve the long-run

relationship between consumption, wealth and income. Therefore, influencing the short-run

behaviour of the South African consumer can shift the long-run relationship (not too

dissimilarly as did the wealth bubble of 2003-2008), thus curbing long-term inflation and

promoting investment-driven medium- and long-term economic growth. Monetary policy in

South Africa can cool household consumption by adjusting interest rates if it is of the opinion

that consumption is either currently too high or set to rise by too high a figure. This then

leads the discussion to a crucial question implicit throughout this study: Is it possible to

forecast next quarter’s growth in consumption?

Using 2�NY as a Predictor of Consumption Growth in South Africa

Using the vector-error correction model approach of Lettau and Ludvigson (2004), the results

of a study into the relationship between consumption, wealth and income have provided the

following answer to the question posed above: the residual of the cointegrated relationship

between consumption, wealth and income may be used to predict next quarter’s growth in

household consumption. When the residual is positive in the current quarter, household

consumption decreases in the next quarter; when the residual is negative today, consumption

is set to increase tomorrow. The major implication of this result is that by applying the

methodology of Lettau and Ludvigson (2004) for South African data, monetary policy

makers may be poised to make more informed decisions regarding interest rate adjustments

in a bid to control inflation and promote economic growth for the South African economy.

7. FUTURE RESEARCH AREAS

The empirical analysis conducted in this study has identified an assortment of additional

areas of research which could be used to further explore the relationship between household

wealth and consumption in South Africa. These are listed and briefly discussed as follows.

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1. This study could be further expanded to include disaggregated wealth data in order to

investigate the separate effects of each form of wealth on consumption in South Africa in

the long-run.

2. Permanent-transitory decomposition of the variables along the lines of Gonzalo and Ng

(2001) could be undertaken in order to further explore the permanent and transitory

dynamics of the shocks to the system.

3. The study could be augmented by using non-durables and services as the proxy for total

consumption, and after-tax labour income as a proxy for human wealth.

4. The study could include panel data to observe the interrelationships between micro

variables within the South African economy.

5. Research into the specific cause, mechanism and aftermath of the wealth bubble of 2003-

2005, with a view to perhaps predicting the mechanism by which the economy will self-

correct following the boom, crash and recovery of residential and equity prices toward the

end of the last decade.

6. Research into how the short-run dynamics of consumption could be manipulated to

positively affect the long-run consumption-wealth relationship in South Africa.

7. Given the high level of socio-economic inequality in South Africa between the rich and

poor, a study could be performed to quantitatively determine the relative burden on each

social sector to increase its short-run saving rate.

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